Simulation of additively manufactured structures on the basis of experimentally determined parameters (OVGU sub-project): Computer models of structures to be manufactured are created at the Institute for Materials, Technologies and Mechanics at OVGU. The additive manufacturing process is simulated using numerical methods, taking into account in particular experimentally determined material parameters and the intermediate crystallization kinetics of the polymers used, whereby the latter are bio-based and biodegradable. In particular, the mechanical and rheological parameters determined in Halle are included in the simulation. Based on the simulation results
(1) the construction of the structures and
(2) the parameters of the printing process
adapted. The components meet the mechanical and geometric requirements of special applications.
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The idea of the project is to develop innovative approaches for purification of emissions of exhaust gas mixtures containing carbon dioxide and other greenhouse gases into the environment by means of separation effects caused by convective instability of the system, to conduct experiments with gas mixtures at different pressures and compositions in channels of different shapes, to conduct theoretical and numerical studies of combined mass transfer of components for model situations and to issue recommendations (composition of mixtures, thermophysical properties, partitioning of the gas mixtures, thermal and thermal properties of the gas mixtures, and other greenhouse gases).

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The objectives of the research project are to develop simplified anisotropic constitutive relations within the coupled distortion gradient elasticity, to determine corresponding scale parameters, to apply such modeling to the solution of some boundary value problems where classical elasticity has its limitations, and to prove that these limitations can be overcome. In detail it is investigated:
- Homogenization problems considering the size effect are considered. In particular, limits as in Voigt and Reuss and as in Hashin-Shtrikman are obtained for particulate composites using the principles of minimum potential energy and complementary energy, effective properties of fiber-reinforced and particulate composites are considered in the framework of the coupled anisotropic
The distortion gradient elasticity is evaluated.
- Crack problems with plane distortion, i.e. crack problems with Mode I, II and III, as well as problems with
with a crack at the edge are examined.
- Problems with concentrated forces, in particular with a half plane loaded on the surface, a force applied in the interior and on the free edge of the plate are analyzed within the framework of the theory.

For all problems, the influence of the coupling term and the anisotropy of the material properties on the solutions, the deviation of the solutions from the predictions of the classical elasticity and from the uncoupled distortion gradient elasticity are investigated. The results are compared in the context of the results available in the literature and
analyzed.
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Digitalization and the energy transition have significantly increased the demand for and complexity of electronic components such as sensors and control units. Wire bonding is used as a basic technology in almost all sectors of industry for the transmission of electrical signals and electrical contacting. When it comes mainly to the transmission of electrical power, high-purity aluminum thick wires with wire diameters between 125 μm and 500 μm are usually used. The wires use so-called wire bridges to connect substrates of different materials with each other, which have different coefficients of thermal expansion. The wires are often exposed to external temperature fluctuations and cyclical loads during operation, which can result in displacement-controlled fatigue loads. This can lead to cracks in the wires and thus to complete failure of the component. [1] It is currently not possible to prevent the failure of wires in highly stressed components by design alone, nor can it be predicted with certainty. For this reason, the aim of this doctoral thesis is to mechanically characterize and numerically describe the real behavior of the wires, taking into account the anisotropic elastic-plastic material behavior, and to predict the application behavior. As part of the doctorate, a mechanical evaluation of the wires will be carried out using tensile, compression and bending tests. The results obtained are correlated with the microstructure of the wires and suitable material models are adapted for the numerical description by means of parameter optimization. In addition, the fatigue behavior of the wires is investigated and the reliability of bonded wire bridges under operating conditions is evaluated using stochastic modeling. The influence of temperature and current density on the wires, as well as their electrical conductivity, will also be considered. All the knowledge and models gained will later be used for the development of new high-performance alloys with improved temperature stability and better electrical conductivity, as well as for the development of alternative wire production routes.
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High-temperature components, such as those found in power plants, must withstand both thermal and mechanical stresses, whereby the combination of these processes can have a negative effect on the service life of the components. Cyclic stresses also occur due to the start-up and shut-down of the systems, the simulation of which leads to numerically complex time integrations with small step sizes. For this reason, the material behavior has so far been simulated with monotonic loads or only for a few cycles, although these can be decisive for fatigue phenomena. The multi-time scale approach is used to model plasticity, damage and fatigue, with the basic idea of creating separate systems of equations for the different time scales by decoupling the equations and solving them separately. A distinction is made between a time scale for quasi-static ("slow") and one for high-frequency ("fast", cyclic) loading. The use of this in combination with a calibrated material model significantly reduces the calculation time and thus not only offers the possibility of considering a high number of cycles, but also results in a more accurate determination and optimization of the service life.
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The demand for light-weight composites is increasing phenomenally especially in aviation, automotive and ship building sectors. As everyone addressed carbon footprints and global warming made by high fuel and energy consumptions and shifting towards specific tailor-made functionally performing materials. This need for light-weight materials is satisfied by honeycomb sandwich laminates as they have proven their advantages over conventional materials with specific weight to strength ratios. With advantage of thermoplastics in high volume production and processability, the sandwich laminates meet the industrial usage. In addition to that the flat semi-finished sandwich laminates are further processable to complex structures to meet different part geometries, with a novel thermoforming procedure by which the sandwich laminate is heated to a thermoforming temperature such that matrix material of face sheet lies above melting temperature and core material lies below melting temperature, then pressed to form into desired geometry. Currently, these materials are investigated for reproducibility in large mass scale owing to the current automation and digitalizing platforms with controlled heating and forming.

Using FEM tools, the manufacturing processes can be optimized by changing the process parameters and material configuration. For this a finite element model is developed considering material, geometry and boundary non-linearities, focused on complex honeycomb geometry and fiber-oriented UD-tapes at meso-scale level. Such developed model is tested for different material combinations, geometries and forming conditions. By this approach the probability of manufacturability of a component through specific technique can be investigated, which saves the material and time in the process of developing a new component. The difficulties in developing such complex model are many like core-face sheet interaction, honeycomb cell walls deformation behavior in melt zones and pre-deformed cell walls during lamination. All these cases will be investigated in this current project.

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The term "homogenization methods" refers to methods that determine the effective material properties of a material with a microstructure from the spatial arrangement of the phases and their individual properties. The prerequisite for this is a sufficient scale interval. The fluctuations of the fields at macro level, e.g. due to geometry variations and boundary conditions, must take place on much larger length scales than the fluctuations in the microstructure. If this is the case, a material sample can be defined on a meso level that is large enough to capture a representative microstructure section. Its effective properties are then applied selectively at the macro level, which is why the material sample must be smaller than the characteristic geometry dimensions at the macro level (Hashin, 1983). In numerical homogenization, the properties of the virtual material sample are determined in a virtual experiment. The latter is referred to as the representative volume element (RVE). By default, periodically continuous RVEs with periodic boundary conditions are used, even for stochastic microstructures. The periodic boundary conditions imitate the embedding of the RVE in an environment with identical material behavior.
This project aims to answer the following questions. How can the three-dimensional stiffness of a material with a microstructure be inferred as accurately as possible if only experiments on thin layers and threads are possible? If the full information of all fields is available in virtual experiments on thin layers, is it possible to deduce the effective properties of the three-dimensional material as accurately as possible by purely numerical means? Can simple estimates such as the already experimentally determined value E_PP2D=E_PP3D ˜ 0.7 be generalized to material classes (polymers), or is this value specific to polypropylene? To answer the first two questions, the development of a homogenization theory for the dimensional transition is required. The third question can only be answered experimentally by measuring E_2D and E_3D on different materials. As has been shown, the local transverse strain is an important indicator for the difference between E_2D and E_3D . Therefore, in addition to the nominal values in the tensile test, the local transverse strain should also be measured on thin films.

Hashin, Z. (1983). "Analysis of Composite Materials - A Survey". In: Journal of Applied Mechanics 50, pp. 481-505.
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The influence of the environment (water, hydrogen etc.) can essentially limit the long-term strength of structural elements due to material degradation. In the case of contacting the different surfaces the deterioration of structural properties continues. The problem of corrosion and wear of machine-building structures has recently been in the focus of attention of researchers and engineers, however, the development of a computational method for estimating the interaction of high-temperature phenomena, such as creep and hidden damage accumulation, continues to be an urgent task. The problem consists in the significant variation of the stress-strain state during long term operation. The existing methods for calculating the strength of structures under the influence of corrosion and wear, as a rule, do not take into account these changes and the accumulation of damage, which can lead to incorrect life estimates.

Structural elements operating at high temperatures under the influence of aggressive media, on the one hand, are among the most expensive, and on the other hand, their failure can lead to environmental damage. This applies to gas turbines and gas turbine engines, automobiles, chemical production equipment etc. Failure and fracture of their structural elements lead to financial losses, is dangerous and unacceptable from the point of view of human safety.

Experimental methods for evaluating high-temperature deformation and fracture under the influence of aggressive media and contact interaction of various details are expensive and often quite hazardous to the health of personnel. That is why the development of a new approach and a numerical method for analyzing creep and damage accumulation in structures affected by corrosion and fretting wear is an important task both at the design stage as well as for the assessing the safe operation time of already operating equipment.

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Powder bed-based laser steel melting has established itself in the additive manufacturing of metallic components. The component is created layer by layer by melting each powder layer and bonding it to the layer below. Due to its high design flexibility, additive manufacturing is used in the aerospace, automotive and many other industries. In view of this, knowledge of the material properties, orientation of the material and the resulting challenges in production are of great importance. Local energy input by the laser, high cooling rates of the melt and the exposure strategy lead to the directional dependence of the material and residual stresses in the components. The resulting distortions have an influence on the manufacturing accuracy. For this, special statements on the mechanical and thermal behavior during and after the process are necessary. The material and material properties, temperature during the process, height, hardness and other parameters play a role here.

The characterization of the thermomechanical behaviour of additively manufactured components is the focus of the doctoral project. Based on continuum mechanical modeling, variant calculations are to show the influence of the various parameters. In addition, a possibility of predicting the properties based on known parameters is to be investigated.
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There is currently no established simulation method for considering crack growth or crack arrest based on an existing technical crack under thermomechanical load. The aim of the dissertation project is to take another important step forward in the simulation-based design of thermomechanically highly stressed components and to develop a simulation method that allows a reliable statement to be made on the further development of the technical crack and thus enables an assessment of the entire service life.

The elaboration is based on the example of a cylinder head consisting of a cast aluminum alloy. The thermomechanical fatigue crack growth depends on numerous different influencing factors. The consideration of crack growth requires on the one hand a clear understanding of the influence and interaction of the influencing factors and on the other hand a robust and industrially applicable integration of the method into the common practice of component simulation in terms of computing time. For this reason, the simulation methodology is to be developed independently from scratch, first with classical FEM and then with XFEM. The validation is carried out step by step in tests with different geometric complexities.
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As part of new approaches to shaping the mobility of the future, electric vehicles in particular have stood out as they can make a significant contribution to protecting the environment and reducing emissions. Electrical steel sheets are used in the construction of traction machines to guide the magnetic flux in the rotor or stator. The magnetic and mechanical properties of the electrical steel sheets are crucial for the efficiency and power-to-weight ratio of the electric machine and are subject to stringent requirements. In addition, low sheet thicknesses of around 0.25 mm and high speeds in dynamic operation lead to high mechanical loads in the rotor.

The openings and magnetic slots required to control the magnetic flux are generally created by punching. Both the shape of the punched edge and the stresses applied during the manufacturing process have a significant influence on the mechanical properties. Due to the coarseness of the material and the unknown shape of the punched edge, the mechanical properties and therefore the component service life can vary greatly.

It is therefore essential to know the cyclical strength properties of electrical steel and how they are influenced by the manufacturing process in order to design electrical steel for operational stability. Through the close cooperation of experimentally verified material investigations and numerical simulation, an efficient and reliable way of predicting the service life of stamped electrical steel sheets is to be developed.

The joint doctoral project of Otto von Guericke University Magdeburg and Ingolstadt University of Applied Sciences focuses on the area of service life calculation and simulation of electrical steel. Key milestones are the service life calculation assuming isotropic material behavior and taking into account locally varying material behavior depending on the punching edge. Finally, the microstructure of the material is to be taken into account in the calculation concept and the methods experimentally validated.
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Theories for slender structures are generally accepted in theory and technology. In engineering, the five-degree-of-freedom model has proven to be particularly useful. It describes disk, bending and transverse shear effects in equal measure. Usually, all considerations are related to a two-dimensional reference surface. Pavel Andreevich Zhilin proposed a so-called direct approach to classical derivation strategies for surface structure theories (dimensional reduction by analytical thickness integration to completely two-dimensional equations), in which all equations are formulated from the outset for a two-dimensional continuum, analogous to the procedure in classical continuum mechanics.

Now that the isotropic elastic material model has already been adequately investigated, the theoretical foundations of surface structure theory with kinematics analogous to Mindlin (1951) are to be expanded. This concerns

1. inelastic material behavior and
2. Direction-dependent material properties.

The extension to include inelasticity will be based on the classic solid laws for viscosity and plasticity. Rheological models for physical description and mathematical formulation have been established here. The greatest challenge lies in describing the behavior in the normal direction. For the viscoelastic behavior there are already results from previous work of the author. If a direct formulation for elastoplastic behavior exists, it should be examined to what extent a viscoplastic material can be represented.

The classical eight symmetry groups are initially used to consider the anisotropy, whereby coincidences can be found with orthogonal projection onto surfaces. However, the general projection of symmetries opens up a far greater variety than can be mapped using classical derivations. Instead of limiting ourselves to special symmetries, the stiffness tensors are to be decomposed in a special way, thus enabling the consideration of arbitrary anisotropic behavior.

Additional expansion possibilities arise in relation to effects resulting from residual stresses, temperature fluctuations and the effects of moisture.
There is a restriction to geometric linearity. So far there is no physical argumentation and mathematical treatment for such extensions of directly formulated theories. The formulations are worked out completely in tensor notation. This enables a direct comparison of the equation structures with three-dimensional continuum mechanics.
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Due to the development of new designs and materials for engines and turbomachines, which are characterized by elevated operating temperatures, it is necessary to estimate the level of irreversible creep strains and the possibility of fracture. In contrast to the previously created general-purpose methods, calculation methods which currently are developed, are aimed at analyzing specific structural elements from specific steels.

The focus of the project is on development a method for calculating cyclic creep and long-term strength and numerical study of the behavior of structural elements operating under the combined action of thermal fields and loads.

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The classical theory of elasticity is an integral part of the daily routine of engineers. It was placed on a firm theoretical foundation between the beginning of the 19th century and the mid-20th century. Its development can be considered complete. Unfortunately, its scope is limited: It is size insensitive, it contains singularities in the stresses and displacements when discontinuities appear in the boundary data, and can not include boundary and surface energies. Thus, it is limited to typical engineering applications. For the description of micro-components or phenomena in the micron- and nanometer range it is only partially suitable.

A natural extension of classical elasticity is the strain gradient elasticity, in which higher derivatives of the displacement field appear. It has been shown in numerous papers that the limitations of classical elasticity theory can be overcome with gradient expansion without blurring the usual separation between structure- and material properties, as is the case with alternative nonlocal theories. Unfortunately, it has not yet been possible to develop a complete solid foundation for gradient elasticity as it exists for classical elasticity theory.

This is not a purely academic matter. The increasing miniaturization of components and the targeted development of micro-structured materials require us to go beyond the classical theory of elasticity. Furthermore, by removing the singularities of classical elasticity, we are able to apply a number of criteria (e.g. fracture and flow criteria), which are usually formulated in the Cauchy stresses, also in the vicinity of boundary discontinuities. This significantly increases the applicability of the elasticity theory.

In this project, the well-established theoretical foundations of classical elasticity are to be expanded to strain gradient elasticity. For this purpose, a generalizing axiomatic theory has been worked out, about 2/3 of which have already been transferred to the gradient theory. We try to complete this transfer, which is the core of the work of the German project partner. The Russian project partner is concerned with specific applications. For example, uniqueness theorems for boundary value problems with pure displacement or pure stress boundary conditions are applied in homogenization. With them, for example, the Eshelby fundamental solution of an elliptical inclusion in an infinite matrix can be extended. Another application are transversely isotropic fiber-reinforced composites, for which both a scale transition and the specific properties of the stiffness tensor are to be investigated. Finally, the de Saint-Venant principle for gradient elasticity will be investigated in beam experiments.

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In the additive production of components made of semi-crystalline polymers, a homogeneous structure without internal interfaces must be achieved in order to avoid distortion effects and to optimize mechanical properties. One starting point is a control of the 3D printing process that is adapted to the polymer. The aim of the research project is to show ways how this can be achieved by combining material understanding, improved process control and suitable component and process simulations. It is being investigated whether and how it is possible to produce more homogeneous components with better properties by adjusting the process parameters to the crystallization kinetics of the polymer used. The crystallization kinetics of available filaments will be quantified in detail, the situation during 3D printing will be detected by inline sensors and the influence of process-related inhomogeneities on the component properties will be quantified by comparing simulation and experiment.

This is a joint project with MLU Halle and the Fraunhofer Institute for Microstructures of Materials and Systems. In this subproject a simulation toolchain for the prediction of inhomogeneous mechanical properties and warpage of components manufactured by 3D printing for the most commonly used polymer filaments is developed, which will be calibrated and verified on the basis of the experimental findings of the project partners. Using a reliable simulation tool, a numerical optimization of the simulated properties can then be performed.

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The availability of novel materials is a key issue for technical innovations, e. g. in energy conversion, mobility or medical engineering. While the effort of R & D in developing new materials was immens over the last years, there is a lack in a detailed understanding of the materials´ behaviour like in complex mechanical stress situations or when exposed to high temperature or radiation. This holds for compact as well for cellular materials.
In order to bridge this gap an integrated approach will focus on the combination of materials processing, materials design, complex stress situations in materials and mathematical modelling. While several of these categories are already combined to each other, R & D of holistic approaches is still in the beginning, and the challenge is to develop connected models which describe the process-microstructure-properties-relationships of materials of different provinience and porosity. Only such a combined approach will allow feedback between materials design and materials behavior.

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The aim of the project is to develop a material model for the martensitic steel alloy X20CrMoV12-1 under high temperatures. For this purpose, hot tensile tests are carried out under constant strain rate, whereby temperature and strain rate are systematically varied. These tests provide the data basis for calibrating and expanding an existing mechanical model that describes the material as a mixture of two phases and takes into account the influence of microstructural processes, such as grain coarsening, on the macroscopic material behavior. Following successful calibration, the model is to be extended to include fatigue processes.
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The manufacturing processes currently available for valve bodies and dosing units are based on a combination of deep drawing + welding. The solid flanges and connections are welded to drawn bases/hoppers and mechanically reworked. For conventional production of the base and funnel, expensive component-dependent drawing tools and powerful presses are required. Incremental sheet metal forming enables the flexible production of complex components at low cost. With the development of the new forming process of spin forming, the production of 3D-formed components with variable sheet thickness from a flat blank without component-specific tools should be possible. The aim is to effectively apply the processes from solid forming methods to sheet metal materials so that the advantageous properties of solid forming, such as fiber flow and work hardening, can be used. As a result, the previously welded component groups are produced as a complex monolithic component with significantly reduced material consumption, weight and costs. Newly developed products, tools and production technology are tested, validated and marketed.
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Background
In the production of thermoplastically formed honeycomb structures, simple standard material equations from various finite element method (FEM) systems fail. Differences to real experiments occur. Furthermore, each honeycomb of the structure has to be constructed, which takes a lot of time.

Objective
>> Creation of a material model that makes it possible to build the structure more simply and to still specify the stresses correctly

Methods
>> Homogenisation of the structure; spring-damper substitute model; use of a representative elementary volume (RVE); transfer of the data into a unit cell

Results
Though not for the application initially focused on, a unit cell was developed which simulates the behaviour of a honeycomb structure.

Conclusions
The work has to be extended not least with respect to a complex check for error causes in order to exclude the individually possible error sources.

Originality
A test environment was created. The determined stress values were homogenised and checked for correctness. Furthermore, the data were used in a unit cell to determine the comparison with the normal structure.

Keywords
Material model, homogenisation, honeycomb structure, polypropylene, viscoelasticity

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The service life of cyclically loaded metallic components is usually limited by the fatigue of the materials used. Partial irreversibility of cyclic deformation leads to strain localization, crack formation and propagation and finally to fracture. In particular, unfavorable orientations of the grains and grain boundaries result in additional stress concentrations, so that local plasticity occurs in the grains even with macroscopically elastic deformations. This cannot be taken into account by conventional macroscopic material models. Of particular importance is the Bauschinger effect, which can be used to describe the direction-dependent hardening of the material. In order to gain a fundamental understanding of the Bauschinger effect, micromechanical and macromechanical tests and microstructural investigations (scanning electron microscopy with EBSD/FIB and transmission electron microscopy) are being carried out by the project partner at the Institute of Ferrous Metallurgy (IEHK) at RWTH Aachen University. On this basis, single-crystal and multi-crystal plasticity models are developed that enable the explicit inclusion of the Bauschinger effect in finite element calculations. The aim is to identify correlations between single and polycrystal hardening. For this purpose, microstructure-based finite element models are examined with regard to the relationship between the kinematic hardening of deformation incompatibilities due to different grain orientations, the ratio of grain size to model size and the kinematic hardening in the individual grain. Based on the results obtained from the microstructure-based calculations, the material parameters of suitable macroscopic plasticity models are determined and correlated with the characteristic values related to the slip systems. By comparing the local residual stress tensors with the macroscopic residual stress tensor, statements can be made about the contribution of inhomogeneity to the Bauschinger effect. Verification experiments on two technically important construction materials (duplex steel 1.4462 and nickel-based superalloy Alloy 718) will demonstrate the possibilities and limitations of the models.
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The sandwich construction with cover layers made of continuous fiber reinforced plastics and structured honeycomb core is the most efficient lightweight construction technology to realize components with minimal weight and maximum mechanical performance. Lengthy production times are still the limiting factor of this lightweight construction technology for cost sensitive markets with large production scales. To close this gap a novel multistage thermoforming process was developed for the processing of flat thermoplastic fiber reinforced sandwich panels into complex shaped sandwich parts in fully automatic manner.

The multistage thermoforming process consists of three main steps, heating of a flat sandwich panel via infrared radiation, robot-guided transfer of the panel into the cavity and thermoforming. The thermoforming step is also divided into three sub-process steps. These are the forming of the sandwich under preserving the characteristics of the core, stabilizing of the formed areas via vacuum gripping to the mold and closing of the sandwich by pressing the edge areas into a compact laminate. The shape of the formed sandwich shell and the transition geometry to the compact laminate can vary to the request of the required part design. To increase the freedom of form, it was also possible to demonstrate in a pilot process that the developed multistage thermoforming process can be combined with thermoplastic injection molding. Both processes together allow to produce complex and ready for use sandwich parts within cycle times of a minute with maximum system utilization.

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Background
The structure-mechanical analysis of such structures still poses major problems, since no adequatetheoryis available and classical continuum-mechanical models lead to immensely high computational complexity. In the context of industrial applications such an effort is not responsible, so the experimental analyses often have to be carried out.

Objective
The main goal of this project was developing a finite element based on a novel shell theory to analyse the sandwich structures with soft core layer (anti-sandwich structures). To achieve such an objective, a robust layer-wise theory for the structural analysis of doubly structures have been used.

Methods
To develop the element, the principal of virtual work was derived according to the layer-wise theory. Next, the shape of the element, the number of nodes, and the number of degrees of freedom have been determined. Afterwards, by choosing adequate shape functions, the source code of the element was written using the Abaqus subroutine user element. Then, the element has been integrated into finite element analyses using Abaqus. At the end, rectangular photovoltaic module were modelled using the new element for verification.

Results
This research deals with modelling the structural behaviour of anti-sandwich shells subjected to mechanical loads. The introduced element (Shell-Lwt) can analyse anti-sandwich structures as plates, single curved shells, and doubly curved shells.

Conclusions
The balance equations and constitutive model for a single layer by using the simple shell theory were obtained. Since mechanical and structural properties of the different layers of photovoltaic panels differ widely, classical approaches for composite structures fail to predict correct results. Therefore, expanding the equationsfor three layered structure was doneusing the layer-wise approach. The result was the formulation of the boundary value problem ofthe overall structure for the three layered composite structure. Since the solution of the formulated boundary value problem in closed form usually tightens a too narrow a frame for practical problems, a procedure for the numerical treatment by meansofthefinite element method was introduced. Therefore, a variational principal was exploited to gain a weak form of governing equations. This form was used to drive the discretized equation of motion. By using a classic finite element type and through the consideration ofartificial stiffening effects, the numerical formulation gained in efficiency and accuracy.

Orignality
The strategy developed here is particularly useful in the design and the development phase of anti-sandwich structures. With the numerical solution approach provided here, it is possible to predict the global structure behaviour as early as in the product development process, which can save high costs for experimental analyses.

Keywords
Curved photovoltaic panel, anti-sandwich structures, simple shell theory, layer-wise theory, finite-element analysis

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The aim of the doctoral project is to identify a suitable material model for the shrinkage analysis of blow-molded plastic hollow bodies and to develop a strategy for calibrating the model. The main difficulty here lies in describing the complex time-, temperature- and process-dependent material behavior of the polymer materials used. Within the project duration, it should first be possible to experimentally characterize the material shrinkage using simple blow-moulded principle components for a broad process window. This experimental database will then be used to calibrate suitable material laws for shrinkage and warpage analysis. The overall aim is to significantly increase the predictive accuracy of the simulation approaches used to date.
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The aim of the research project is to clarify the effect of stationary temperature gradients - and associated stationary thermally induced stress gradients - on the damage development of cooled high-temperature components. This stress characteristic typical of turbomachinery is not yet fully understood, particularly with regard to its contribution and its consideration in damage assessment. Corresponding deformation and damage models must be created and validated. A possible analogy to the assessment of geometric notches is also to be investigated. Furthermore, it is planned to shorten the necessary
to provide a validated extrapolation method for the calculation times of component models
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Pistons and cylinder heads made of cast aluminum materials in internal combustion engines are subject to strong temperature changes during use, which lead to thermomechanical fatigue (TMF). The combustion process results in additional high-cycle fatigue (HCF), which is superimposed on the thermal cycles and results in a combined TMF/HCF load. For cast aluminum alloys, it is known that a TMF/HCF load leads to a significant reduction in service life compared to a pure TMF load. As part of the project, detailed material investigations were carried out on the fatigue behavior and damage development of two cast aluminum materials. Based on the test data and the observed damage development, a short crack growth model was developed and adapted to the specific damage mechanisms of the two materials. The short crack model can describe the lifetimes of a large number of sample tests very well.
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The microstructure of the precipitation-hardened aluminum alloy EN AW-2618A is of outstanding importance for its strength, as only a material condition with a specifically adjusted microstructure achieves sufficient strength for centrifugal compressor wheels. However, this optimized microstructure changes during operation, as the components are used at temperatures that are close to or even exceed the hardening temperature. As the microstructure ages, a degradation of the properties can be observed. The present work describes the degradation of the material's strength in three application-relevant areas: cyclic plasticity at elevated temperature, LCF fatigue life and creep. Based on experimental results, models are adapted and discussed for application in a finite element context.
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Photovoltaic modules are multi-layer panels for which conventional approaches cannot be used. New analysis approaches are to be established as part of the project. Multiscale approaches will be used. The modeling is initially limited to elastic material behavior.
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The aim of the project is to describe the failure of an iron aluminide coating, which is applied to an aluminum alloy and tested between 250^oC and 400^oC. To validate the developed model and identify the required material parameters, four-point bending tests are used, which are carried out in the specified temperature range and under different loads. In addition, these tests also form the basis for deriving the model. Failure modeling is based on the theory of the cohesive zone, which was developed independently by Barenblatt (1959) and Dugdale (1962). The developed models are implemented in the simulation program ABAQUS using the UEL and UMAT interface. Furthermore, the efficiency of different solution strategies for the resulting partial PDE system is investigated in the project. The quasi-static calculation in combination with a viscous regularization represents the most efficient strategy. Figure 1 shows the comparison between the experiment and the simulation (circles), whereby a correction of the creep multiplier is necessary for a better match (triangles).
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The geometrically complex flame protection filters prescribed for commercially operated thermal appliances and kitchen equipment must not only ensure the separation of free-floating aerosols, oil and emulsion mists and dust particles, but also flame transmission. The design and performance requirements are constantly increasing due to higher temperatures during cooking processes, the reduced upper limit for particulate matter and new aerosols and oils. Previous manufacturing processes did not allow for cost-efficient production, especially for small quantities and installation heights of less than 50 mm.

The aim of the project was to develop a new technology and modular tools for the flexible production of new types of flame-retardant filters with maximum flame-arresting properties, up to 30% higher separation efficiency even with particle diameters = 5.0 µm and with minimal assembly effort thanks to quick connections. For various size ranges and installation heights from as little as 20 mm, flame-retardant filters can be produced economically and efficiently, even in very small quantities. The dead weight can be reduced by approx. 25 % and the cost-effectiveness of production increased by approx. 15 %.
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Scientific and applied goal of project is to derive a physical model  and to develop a tool for numerical simulations, that allows through the control of crystallization parameters during an injection molding process to obtain an optimal mechanical properties for a polymer-based mechanical part. It requires clear understanding of relationships between (i) mechanical properties of injected mechanical components, (ii) knowledge about internal structure of spatial inhomogeneous particularly crystallized mechanical parts and information about process parameters, that were used during the injection molding procedure.  The project is focused mainly on influence of thermal regimes.

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The principal objective of the proposed research is to expand the modeling capabilities of CNTRM s considered in the current project (and other composites with interphases) into an inelastic range. More specifically, the goal is to develop a method of evaluating the overall nonlinear behavior of CNTRM´s associated with damage of its interphases. This choice is made in recognition of the fact that damage, particularly damage of the interphases is an important aspect of nonlinear behavior of composites. As opposed to this approach, however, where discrete analysis of progressive debonding along the interphase was considered for representative unit cell (RUC) of a composite with regular arrangement of inhomogeneities, in this work a continuum approach to damage will be adopted. This appears to be a natural approach for composites with random microstructure, where RUC cannot be identified, and it is novel in the existing literature on the subject.

Another specific objective of the approach proposed here is to devise an approach suitable for materials with random arrangement of CNTs and their finite aspect ratio. Unlike random arrangement of spherical inhomogeneities, where the zones of debonding for a typical inhomogeneity can be associated with the principal directions of loading, such association cannot be realistically assumed in the case of CNTRM. In CNTRM the local elastic fields may very much more significantly and it is meaningful to describe the problem in terms of statistical averages. These averages represent the entire collection of CNTs in the material, each of them may have somewhat different pattern of damage. Collectively they should be equivalent to inhomogeneities whose interphases undergo homogeneous (smeared) damage. This assumption forms the basis for the approach proposed here, and, in fact, it parallels the thinking pursued in phenomenological 3D continuum description of damage. The difference is that the averages of elastic fields used in the formulation of the problem are based on the designed, or measured, statistical distribution of inhomogeneities (CNT) and are anticipated to lead to a material-tailored description.

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Many materials or media in nature and technology possess a microstructure, which determines their macro behaviour. Despite of possible difficulties to describe the morphology of this structure, the knowledge of the relevant mechanisms is often more comprehensive on the micro than on the macro scale. On the other hand, not all information on the micro level is relevant for the understanding of the macro behaviour. Therefore, averaging and homogenization methods are needed to select only the specific information from the micro scale, which influences the macro scale. These methods would also open the possibility to design or to influence microstructures with the objective to optimize their macro behaviour. Study and development of new methods in this interdisciplinary field of actual research will be under the supervision of professors from different engineering branches, applied mathematics, theoretical, and computational physics.

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Photovoltaic systems are multi-layer plates for which classical approaches cannot be used. New analytical approaches are to be established as part of the project. On the one hand, multi-scale approaches are used. The modeling is initially limited to elastic material behavior.
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The main goal of the project is presentation of a new approach to modeling and homogenization of random Carbon NanoTube (CNT) - reinforced materials. The secondary goal is to demonstrate the effectiveness of that approach in its application to analysis of stress/strain fields in composite structural elements.
In the proposed model CNT-s will be assumed to be dispersed within the matrix material in a prescribed random manner, characterizing the material of interest (and obtained from experimental observations, for instance). Microstructure of the material will be described by probability functions specifying volume fraction of CNT-s, their orientations, dimensions and other relevant parameters. From the viewpoint of mechanics CNT-s will be modeled as hollow ellipsoidal or cylindrical nano-inhomogeneities, with a layer of graphene forming their surfaces and interacting with the matrix material.
Mathematically, the homogenization problem will be formulated by coupling equations of bulk elasticity with equations of the materials surface model which accounts for the specifics of the CNT-reinforcement. The coupling between these two sets of equations will reflect the nature of bonding between CNT-s and the matrix, which is the least explored and, thus, most uncertain part of the model. For that reason, two different ways of accounting for various bonding conditions between CNT-s and the matrix will be investigated and compared.
One way will consist in inserting between CNT-s and the matrix a thin, continuous layer of elastic material whose properties will be adjusted so as to emulate the properties of bonding. The parameters used in the description of that thin layer will be determined from linearization of appropriate inter-atomic potentials. The second way will be via modified properties of CNT-s themselves, which will combine the original properties of CNT used in the first approach and those of bonding. In the second approach the need for an additional layer will be eliminated.
The statistical method of conditional moments, in conjunction with the probability functions describing the material, will be used in evaluation of the governing equations to extract closed-form expressions for effective elastic moduli (size-dependent) of CNT-reinforced material. Several specific materials will be analyzed, their effective properties determined and comparisons with the existing results will be made.
As an illustration the proposed model will be used in the structural FEM analysis to predict the behavior of composite structures whose geometry and loading are relevant to applications. Specifically, a plate without and with a central circular hole subjected to an in-pane loading will be investigated. It will be demonstrated how variations of geometrical parameters, volume fraction, spatial distribution, orientation and bonding of CNT-s change the structural behavior and how it may be beneficial in optimal design of those structures.

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Cylinder heads in vehicle engines are not only exposed to high mechanical stresses, but also to high thermal stresses. The cyclic loading of the component results in large local temperature differences and consequently also considerable stress gradients, which can have a damaging effect on the component. In this project, a model similar to a component is initially being developed, which can be used to depict fundamental influences. Furthermore, the behavior of the resulting damage is to be calculated with the help of XFEM and the existing impairments are to be made assessable. In addition, the calculation model should be transferable to other components and materials.
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Aircraft turbine components such as turbine blades and disks are exposed to high thermal and mechanical stresses, which can cause stresses and local plastic strains. The combination of temperature transitions with mechanical expansion cycles leads to thermomechanical fatigue of the material and thus to increasing damage during operation, which can lead to component failure after a certain number of cycles. In order to achieve a weight reduction in the development of new turbines under these high material loads and at the same time an increase in efficiency through higher temperatures, reliable calculation methods for service life prediction are required. For service life prediction, a plasticity model is generally used, the material parameters of which have been determined in such a way that experimentally determined stresses and strains of the material are well described on average by the model. The stresses and strains deterministically calculated with the plasticity model represent input variables for a damage model, which in turn is used to deterministically describe the service life measured for the material on average. The scatter in the material behavior of different material samples and their influence on the service life prediction of highly stressed components cannot be evaluated using this procedure. This results in uncertainties in component design, which can lead to both over-conservative and non-conservative component evaluations. For this reason, a methodology for probabilistic service life prediction is being developed in this project, which enables the influence of scattering in material behavior on service life to be quantified. Statistical methods and a mechanism-based damage model are used for this purpose.
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Many tool damages that occur during hot forming in operation are due to fatigue cracks. The fatigue cracks form and grow due to the high localized cyclical thermal and mechanical stresses on the tools. To date, there is no established simulation methodology for the computational evaluation of the service life of forming tools that allows reliable statements to be made regarding the number of cycles that can be endured for failure under different stress conditions. The aim of the proposed project is therefore to develop advanced material models for assessing the service life of hot forming tools and to test their predictive power using industry-related applications. Based on experimental investigations carried out at the Institute of Forming Technology and Machines IFUM at Leibniz Universität Hannover, the material data required for the modeling of a widely used tool steel will be determined and its damage behavior investigated. On the other hand, advanced material models for the numerical description of the measured deformation behavior are used and further developed in theoretical work. A model based on the observed damage mechanism, which can take into account the influence of different load situations, is to be derived specifically for service life assessment. The models are to be implemented in commercial finite element programs and validated using two different industry-related applications. In the future, the developed models should enable a computational service life assessment for the safe design of hot forming tools.
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The aim of the project is
1) to develop mathematical models of plates and shells taking into account surface stresses acting in surface layers, coatings, phase transitions, non-homogeneities with engineering applications;
2) to develop mathematical models of generalized media such as Cosserat continuum, micromorphic continua, second-gradient media.

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Advanced chromium steels are widely used materials for components in power plants. Due to their complex microstructure these steels show a good creep resistance. Nevertheless a reliable prediction of the deformation state caused by temperature and thermal load is essential in the design process of power plant components. To this end a material model based on a continuum mixture theory approach is utilized. Therefore the microstructure is represented as an inelastic hard and inelastic soft phase to derive constitutive equation of the mixture. Furthermore evolution of the microstructure is described by evolution equation of inner state variables, which enter the constitutive equation. Material model parameters are calibrated against uni-axial material tests for different stress and temperature levels. For verification purpose the calibrated material model has to predict material behavior for non constant stresses. Finally the material model will be implemented in a commercial FE-code to perfume the structural analysis of component.

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Since 1970s, phases in the Ti-Al alloy system have been widely recognized as a possible basis for the development of novel lightweight alloys for high temperature structural applications. These alloys exhibit impressive material properties such as high strength, fracture toughness, corrosive resistance, low density and high melting temperature. Because of these properties, Titanium alloys are widely used in numerous structural applications, particularly in aerospace application such as low pressure turbine blades, high pressure compressor blades, vanes, casings and tiles etc. From available different titanium alloys, gamma-TiAl type (with FCC structure) and alpha2-TiAl ( with CPH structure) alloys show superior properties. At the moment, the alloys with the best overall mechanical performance are based on the intermetallic, gamma-TiAl phase strengthened by minor fractions of the hexagonal αlpha2-TiAl phase and hence it is one of the most popular alloys used in aerospace application.

With the constraint of cost and time, modeling of alloys becomes priority to study the material response in extreme conditions of high stress and temperature, particularly in creep. Thermomechanical fatigue life prediction is also an important part in the design of high temperature materials and requires a stress-strain analysis for accurate results. The modern methods for life prediction in structures need inelastic analyses, which lead to much progress made in the development of constitutive equations to represent the mechanical response of materials under various loading conditions at high temperatures.

In short, the inelastic behavior like yielding, hardening, creep, relaxation etc. of mentioned Ti-based alloy will be investigated in detail by using the crystal viscoplasticity model and compared with experimental results. Representative Volume Element (RVE) is to be used with periodic boundary condition since plane and symmetric boundary conditions can not give the possibility to use complex loading condition experienced in practical application. Specific parameter determination protocols are will be established for crystal viscoplasticity model implemented in ABAQUS through a user material subroutine. This research will focus on the development, numerical implementation and application of two distinct versions of viscoplasticity, classical crystal plasticity and dislocation-based continuum dislocation theory in the context of Ti-Al alloy, the size-dependent deformation and temperature dependence are also to be studied via direct numerical simulation.

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Teilprojekt: Modellierung der Kriechschädigung bei nichtproportionalen Beanspruchungen  
Bearbeitung: Frau O. Ozhoga-Maslowska  
Betreuung: H. Altenbach, K. Naumenko  
Ausgehend von Mechanismen der Hohlraumbildung und des Wachstums sowie einer ange­nommenen Gefügegeometrie (Körner, Korngrenzen, Partikel) soll ein mikromechanisches Modell entwickelt und verschiedenen Beanspruchungszuständen (ein-, mehrachsig, Zug- und Druckbeanspruchung, variable Hauptspannungsrichtungen) unterworfen werden. Insbesondere soll die Mehrachsigkeits- und Spannungszustandseinflüsse betrachtet werden. Darauf basierend sowie mit Hilfe einer Homogenisierung sind geeignete tensorwertige Schädigungsvariablen sowie entsprechende Evolutionsgleichungen zu entwickeln.

Teilprojekt: Mechanismen-basierte Modellierung hochlegierter warmfester Stähle  
Bearbeitung: Adill Maimati  
Betreuung H. Altenbach, K. Naumenko  
Ausgehend von den Kenntnissen der kriechverzerrungsinduzierten Gefügeänderungen (Vergröberung der Subkornstruktur, Vergröberung von Karbidausscheidungen etc.) sowie in der Werkstoffkunde diskutierten mikromechanischen Modellen (Verbundmodelle für kriechharte und kriechweiche Bereiche, Evolutionsgleichungen für Versetzungsdichte), soll ein mehrachsiges  Modell, das für die Simulation von Großbauteilen einsetzbar ist, entwickelt und verifiziert werden. Zu diesem Zweck ist das Konzept eines mehrphasigen Mediums (Mesomodell) heranzuziehen. Die Konstitutivgleichungen der Bestandteile (hart und weich) sind separat zu formulieren und mit Methoden der Kompositmechanik (Mischungsregeln) zu kombinieren. Da die Volumenanteile von mikrostrukturellen Größen, z.B. mittlere Subkorngröße, abhängig sind, sollen entsprechende Evolutionsgleichungen formuliert werden. Das Makromodell (Modell mit einem Rückspannungstensor und Entfestigungsvariablen) ist durch eine geeignete Mittelung zu formulieren.    

Teilprojekt: Mikro-Makro-Untersuchungen des anisotropen Kriechverhaltens in einer mehrlagigen Schweißnaht  
Bearbeitung: Ivan Lvov  
Betreuung H. Altenbach, K. Naumenko    
Ausgehend von den Konstitutivmodellen und experimentellen Daten zum Kriechen der einzelnen Gefügezonen soll ein mikromechanisches Modell für das mehrlagige Schweißgut entwickelt werden. Mit Hilfe der FEM-Simulationen ist das Kriechverhalten unter gegebenen ein- und mehrachsigen Spannungszuständen numerisch zu simulieren. Dabei ist zu klären, welchen Einfluss die angenommene Gefügegeometrie (Geometrie der Lagen, Breite der Wärmeeinflusszonen) hat und wie sich die Variation dieser Geometrie auswirkt.   Darauf basierend ist ein makromechanisches Konstitutivmodell, das sowohl die Ausgangsanisotropie als auch die schädigungsinduzierte Anisotropie beachtet, zu formulieren. Das Model wird anschließend für eine Schweißnahtanalyse eingesetzt.

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Estimation of behavior of metal closed-cell foams under compressive loading is a complex task and must take into account buckling problem, plastic deformation of the cell walls, self-contact problem, damage accumulation, arising cracks and their growth, etc. Full map of the problem is such complicated,  that its direct solution is very expensive for application in the industry.

In the work in proposed simplified scheme for estimation of arising in the metallic closed-cell foams strain localizations and packaged domains of cells. The work is divided on two main parts. First part is devoted to the nucleation problem of strain localizations and based on the solution of the linear buckling problemfor closed-cell metallic foammodeled bymeans of Voronoi tessellation. In the second part is discussed themodeling of packaging propagation in themetallic closed-cell foams. Modeling is based on the phase-field approach. Verification of proposed estimation scheme is performed on base the of experimental data for aluminumclosed-cell foamAlulight®.

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Polymers enable high-volume production at low production costs compared to components made of metallic materials. This economic advantage makes polymer components interesting for the automotive supply industry. Due to the mechanical properties of polymers, significant creep effects occur even at low load levels, moderate thermal loads and short holding times.

The non-linear material behavior of polymers must be taken into account in the component design process. In addition to real component tests, the simulation of components is an essential part of the dimensioning and design process chain. A potent material model must be available for realistic simulation results.

The polymer POM is being investigated for Robert Bosch GmbH. The material behavior is to be identified on the basis of individual creep curves. The material model is formulated in 1D for finite deformations and then extended to 3D. The 3D formulation is implemented in the FE code Abaqus and the material model is verified by means of component tests.
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Constitutive models for the description of the inelastic material behavior in the high temperature range are developed for cast iron composites. For this purpose, concepts of continuum mechanics of multiphase media are used. The material properties in the models are identified on the basis of experimental data (hot tensile tests and creep tests)
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Das wesentlichen Ergebnis der Dissertation ist die Analyse spiraler piezoelektrischer Nanofilme und eines Massivs aus Film/Kristall. In Ergänzung dazu wurden Simulationen des Verhaltens betrachtet,  insbesondere bei Berücksichtigung des Einflusses äußeren Mediums. Entsprechende Simulationen können ausschließlich numerisch vorgenommen werden, da analytische Lösungen nicht existieren.

Folgenden Ergebnisse  (Auswahl) wurden für die Modelle der Nanostrukturen mit der chiralen Elementen erzielt:

- Ein Modell für ein- und mehrschichtige Strukturen mit Spiralgeometrie und mit besonderen Materialeigenschaften
wurde  entwickelt. Das mathematische  Modell gründet sich auf kontinuumsmechanischen Überlegungen. 

- Die Simulation sowohl des direkten als auch inversen piezoelektrischen Effekts unter Berücksichtigung der
verschiedener piezoelektrischen Eigenschaften wurde vorgenommen. Auch wurde der Einfluss der Polarisation und der Geometrie des Films im Rahmen der elastischen und elektrischen Aufgaben betrachtet. Die grundlegenden unbekannten
Systemparameter wurden bei der numerischen Simulation erhalten.

- Das Eigenwertproblem mit der Bestimmung der Eigenwerte und jeweilige Eigenmoden des Nanoschale wurden erhalten. Die Ergebnisse des beschriebenen Eigenwertproblems geben eine gute Übereinstimmung mit Ergebnissen, die in Arbeiten von Eremeyev u.a. in den Jahren 2005-2007 erzielt wurden.

- Das Problem der Wechselwirkung der piezoelektrischen Schale mit einem  nicht-linearen Medium  ist vollständig gelöst
worden. Dabei wurde numerisch eine Methode verwendet, die auf dem Zwei-Wege-Austausch zwischen Finite-Elemente- und Finite-Volumen-Verfahren beruht.

- Der unterschiedliche Einfluss einer Newtonschen und nicht-Newtonschen Flüssigkeit wurde untersucht.  Zwei Modelle sind für die parametrische Analyse der Interaktion einer schraubenförmigen Membran mit einem äußeren Medium
vorgeschlagen worden.

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Der Energiebedarf des Menschen wird immer größer. Die natürlich vorhandenen Energieressourcen sind in einer Form in der Natur und verlangen nach Umwandlung in eine Form, die leicht zugänglich für den Endverbraucher ist. Kraftwerke spielen u.a. eine Rolle in diesem Umwandlungsprozess. Die Umwandlungsprozesse müssen zwei wichtige und aktuelle Probleme einbeziehen - sie sollten hocheffizient und umweltfreundlich sein. Um diesen Anforderungen gerecht zu werden, ist die Mehrheit der Umwandlungsprozesse durch hohe Temperatur und Druck gekennzeichnet. Allerdings haben diese Bedingungen großen Einfluss auf die Lebensdauer und das ordnungsgemäße Funktionieren der Kraftwerkskomponenten in den Energieumwandlungsprozessen. Typische Folgen sind inelastische Materialverhaltensweisen wie Kriechen und Ermüdung in den Werkstoffen, aus denen die Kraftwerkskomponenten bestehen.

Im Projekt wird sich auf die Modellierung des inelastischen Verhaltens konzentriert, wbei die Anwendung sich auf Wärmetauscher bezieht. Es wird ein inelastisches konstitutives Modell für den T91 Stahl entwickelt - der Stahl ist typisch für den Kraftwerksanlagenbau. Die Parameter in den Modellgleichungen sind identifiziert worden und das Modell zeigt gute Übereinstimmung mit Versuchsdaten. Ein Material-Benutzer-Unterprogramm ist geschrieben worden, um das Modell in die kommerziellen Software ABAQUS zu integrieren. Das Modell wurde verwendet, um das Kriechverhalten einer gekrümmten Rohrleitung aus T91 Stahl zu simulieren.

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Kraftübertragende dünnwandige Bauteile werden häufig aus kurzfaserverstärkten Polymeren im Spritzgussprozess hergestellt. Während der Formfüllung entsteht eine Mikrostruktur bevorzugter Faserorientierungen, die zu einer Anisotropie der mechanischen Eigenschaften führt. Um im Stadium der Auslegung eines Bauteils Voraussagen über die Eigenschaften machen zu können, muss die Faserorientierung mit Hilfe von Simulationsprogrammen vorhergesagt werden können.Die Bewegungsgleichung für die Rotation eines einzelnen Partikels im strömenden Medium wird hergeleitet und numerisch gelöst. Dabei wird die Wechselwirkung des Partikels mit dem umgebenden Medium berücksichtigt.

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The project aims at continuation and advancement of activities initiated in FP6 ToK project MTKD ? CT - 2004 ? 014058 at the Centre for Modern Composite Materials (CMCM) created at the Lublin University of Technology (LUT). It is planned: a) to unlock and develop the full research potential and increase research capacities of the CMCM staff in the areas of competence comprising modelling of composite and smart materials and their applications to aerospace and  transport infrastructure (pavements and airfields), also modelling and control of dynamics of structures made of composites b) to establish new areaof competence: innovative technologies for manufacturing of composites, c) to upgrade research equipmentfor testing of composite materials. The project objectives will be accomplished by a coherent set of the following complementary actions: twinning collaboration, recruitment of experienced researchers, organisation of workshops and mini-symposia, participation in international conferences, purchase of equipment. The project implementation will result in creating a leading research centre in the Middle-East part of Europe in the multidisciplinary area encompassing modelling and experimental testing of composite and smart materials and their application to aircrafts, pavements and airfields. The proposed project will strengthen co-operation with the regional industry, in terms of socio-economic aspects: will help to compensate disproportion (Lublin region is a less favoured one). It is also envisaged that the project will increase visibility and competitiveness at international level of the CMCM in the field of composite materials and their applications to engineering structures, resulting in deeper involvement of the CMCM in FP7 projects and better integration of the CMCM in the ERA.

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Ziel des Projectes ist es, dass inelastische Verhalten von Schäumen besser zu beschreiben. Dabei wird von einer direkt formulierten Schalentheorie ausgegangen (Cosserat-Ansatz), da hauptsächlich dünnwandige Flächentragwerke untersucht werden sollen. BBeim inealstischen Werkstoffverhalten soll exemplarisch das viskoelastische Verhalten betrachtet werden.

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Polymers enable high-volume production at low production costs compared to components made of metallic materials. This economic advantage makes polymer components interesting for the automotive supply industry. Due to the mechanical properties of polymers, significant creep effects occur even at low load levels, moderate thermal loads and short holding times.
The non-linear material behavior of polymers must be taken into account in the component design process. In addition to real component tests, the simulation of components is an essential part of the dimensioning and design process chain. A potent material model must be available for realistic simulation results.
The polymer POM is being investigated for an industrial partner. The material behavior is to be identified on the basis of individual creep curves. The material model is formulated in 1D for finite deformations and then extended to 3D. The 3D formulation is implemented in the FE code Abaqus and the material model is verified by means of component tests.
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Das Konzept der Vergleichsspannung ist von grundsätzlicher Bedeutung bei der Bewertung der Festigkeit, des plastischen Fließens oder des Versagens. Die traditionellen Konzepte genügen im Falle der Konstruktionswerkstoffe, die oftmals bis heute eingesetzt werden. Im Fall von neuen Werkstoffen müssen die Fragen der Kompressibilität, des unterschiedlichen Zug- und Druckverhaltens u.a.m. überdacht werden.

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Generalized continua were discussed 2 years ago during the first trilateral seminar (see Altenbach,H.; Erofeev,V.;Maugin,G.A. (Eds.):Mechanics of Generalized Continua. Advanced Structured Materials, Vol. 7 - Berlin: Springer, 2011). Frome September 26th up to September 30th, 2012 the second seminar will held in Wittenberg.

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In recent years significant progress in synthesis of metamaterials with perspective and unusual functional properties is observed. The properties of these metamaterials are highly depend on their microstructure. In particular, the helical shell structures have found various applications, for example in MEMS/NEMS, optics and medicine. The interaction of the shell with the environment is highly important for engineering design, e.g in the medicine applications when the shell operates in fluid. The model of non-Newtonian fluid of pseudoplastic type is used. We examine the types of motion of the shell in laminar flows. The research is taken into account the piezoelectric properties of the helical shells. Principal task is the simulation of the shell kinematics in the some non-classical environment. The second part of the work consider nanocrystal/nanofiber arrays and apply the applications of the classical mechanics of fibre reinforced composites taking into account the morphology and electrical properties of nanocrystalls. In addition, for irregular structures the fractal analysis is applied. Unlike to the classical composites in this work also taking into account the interaction forces between the nanocrystals such as van-der-Waals forces, adhesion forces, etc. The interaction between first and second part of the research consist in the micro-macro interaction between shell and array of the shells.

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Schäume sind typische Vertreter von Werkstoffen mit Anwendungen im Leichtbau. Dabei gibt es unterschiedliche Varianten: offenzellige oder geschlossenzellige Schäume; Polymer- oder Metallschäume. Allen gemein ist, dass durch die "Porosität" die mechanischen Eigenschaft im Vergleich zu Bulkmaterialien deutlische unterschiede aufweisen. Im Mittelpunkt des Projektes steht das inelastische Verhalten, was u.a. mit der Einheitszellenmethode simuliert werden soll.

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Ziel der Arbeit soll es sein, eine Methodik zur Beschreibung des Langszeitverhaltens von kurzfaserverstärkten Kompositen zu finden. Dabei soll mit Hilfe einer 2-Skalenmodellierung versucht werden, nur aus den Eigenschaften der Konstituenten und des Orientierungszustandes der Fasern, den Komposit zu beschreiben. Im Anschluss sollen die gewonnenen Erkenntnisse in das FE Programm Abaqus mit einer Materialsubroutine eingebaut werden.

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Das Langzeitverhalten von 9%-12% Cr warmfesten austenitischen Stählen wird untersucht. Dazu wird ein entwickeltes Modell anhand von Literaturdaten kalibriert und in den kommerziellen FE-Code ABAQUS implementiert. Es werden ausgewählte Benchmark-Probleme gelöst und mit Literaturdaten verglichen. Nach den erfolgreichen Benchmarks werden Bauteile mithilfe des
Modells berechnet.

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Phasenumwandlungen stellen ein hochinteressantes Forschungsgebiet mit zahlreichen Anwendungen dar. Im Rahmen dieserArbeit sollen hauptsächlich die kontinuumsmechanischen Grundlagen untersucht werden.

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In der Lutherstadt Wittenberg findet das erste trilaterale Symposium mit 30 Teilnehmern aus Deutschland, Frankreich und Russland statt. Im Rahmen des Symposiums sollen verallgemeinerte Kontinua diskutiert werden, deren Grundlagen u.a. in den drei Ländern entwickelt wurden.

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Innerhalb des Graduiertenkollegs wird das inelastische Verhalten von Aluminiumlegierungen des Automobilbaus bei zyklischer Beanspruchung experimentell charakterisiert und numerisch simuliert. Dabei liegt der Schwerpunkt auf einer niedrigen Zyklenzahl. Gleichzeitig werden jedoch erhöhte Temperaturen vorausgesetzt, die zum inelastischen Verhalten führen.

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Konstruktionen des Maschinenbaus unterliegen of komplexen Beanspruchungen. Dies betrifft die Art der Beanspruchung (rein-mechanisch), thermisch usw.  Gleichzeitig ist die Mehraxialität des Problems von Bedeutung. Werkstoffwissenschaft und .physik beschreiben das Materialverhalten oft nur eindimensional. Innerhalb des Projektes werden insbesondere mehrachsige Stoffgesetze untersucht und auf ihre Anwendbarkeit geprüft.

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The subject of the research project is the investigation of the
mechanical properties of elastic shells and plates endowed with a
certain microstructure. In this sense, we employ the model of
deformable directed surfaces, which is effective for the study of thin
bodies with complex internal structure. The objectives of the research
project are the following:
1. to investigate the mathematical aspects of the theory of deformable
directed surfaces: we study the boundary-initial-value problems associated
with the deformation of elastic shells and study the significant
properties of their solutions concerning existence, uniqueness,
reciprocity, variational characterizations, and continuous dependence on
the external loads;
2. to extend this approach for the modeling of shells made of porous
materials or other microstructural materials.

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Recently, the theory of elasticity with surface stresses was developed for nanomechanical problems. Within this theory, the surface stresses act on the body boundary.

In our researches we extend the linear theory of elastic shells for this case. We obtained the equations of equilibrium and constitutive equations for the stress resultants and couples tensors while taking into account the surface stresses acting on the shell surfaces. The effective shell stiffness, in particular, the bending stiffness depends here also on the surface elastic moduli, which is substantial for nanodimensional thicknesses. We also consider the effective stiffness properties of the nanoporous materials like as nanofoams.

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Metallic and polymer foams are widely used in modern industries, e.g., the aircraft and the automotive industries, but also with other application fields like biomechanics. The reason for this is some specific properties of these advanced materials. They are very light, but the specific strength is comparable with the classical structural materials. If they are applied as sandwiches, the specific properties can be even much better. In addition, they are able to absorb energy which allows the use of these materials as crash elements.

In general, technological parameters in foam production are adjusted such that a uniform effective foam density is achieved throughout the products. Some technologies, e.g., injecting foam in a cavity or filling a mold with foam by an expansion process, naturally result
in non-uniform distributions of the effective density. These inhomogeneities
of the effective foam density may be exploited in structural
design, essentially treating the foam as a functionally graded material.

FGMs are composite materials where the composition or the microstructure
is locally varied so that a certain variation of the local
material properties is achieved. Modern FGMs are constructed
for complex requirements, such as the heat shield of a rocket or implants
for humans. In these cases the analysis of the material and
the structures made of FGMs cannot be only limited to the mechanical
behavior. FGMs can be modeled as a porous material with nonhomogeneous
distribution of porosity.

Engineering structures made of porous materials, especially metal
foams, have been used in different applications in the last decades.
A metal foam is a cellular structure consisting of a solid metal, for
example aluminium, steel, copper, etc., containing a large volume
fraction of gas-filled pores. There are two types of metal foams. One
is the closed-cell foam, while the second one is the open-cell foam.
The defining characteristics of metal foams are a very high porosity:
typically well over 80%, 90% and even 98% of the volume consists of
void spaces.

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Polymer- und Metallschäume besitzen ein hohes Innovationspotential. Sie werden verstärkt in Luft- und Raufahrt, aber auch in der Automobilindustrie als Leichtbauwerkstoffe eingesetzt. Ziel der Studie ist eine Auseinandersetzung mit den unterschiedlichen Modellierungen auf der Mikro-, Meso- und Makroebene. In einer ersten Stufe sollen die theoretischen Überlegungen in ein makroskopisches Werkstoffmodell eingehen, wobei dieses dann im Sinne vonn effektiven Eigenschaften im Plattenmodell verwendet wird. Erste Ergebnisse der statischen und dynamischen Globalanalyse haben gezeigt, dass die Kirchhoffsche Plattentheorie in einigen Fällen versagt und zu verbesserten Theorien übergegangen werden muss.

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Kraftübertragende dünnwandige Bauteile werden häufig aus kurzfaserverstärkten Polymeren im Spritzgussprozess hergestellt. Während der Formfüllung entsteht eine Mikrostruktur bevorzugter Faserorientierungen, die zu einer Anisotropie der mechanischen Eigenschaften führt. Um im Stadium der Auslegung eines Bauteils Voraussagen über die Eigenschaften machen zu können, muss die Faserorientierung mit Hilfe von Simulationsprogrammen vorhergesagt werden können.Die Bewegungsgleichung für die Rotation eines einzelnen Partikels im strömenden Medium wird hergeleitet und numerisch gelöst. Dabei wird die Wechselwirkung des Partikels mit dem umgebenden Medium berücksichtigt.

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Maschinenbaukonstruktionen unterliegen unterschiedlichen Belastungen, wobei u.a. nach statischen, quasistatischen und dynamischen unterschieden wird. Im Rahmen des Projektes wurden die unterschiedlichen Konzepte miteinander gegenübergestellt und Gemeinsamkeiten herausgearbeitet.

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The project aims for establishing new areas of competence at Lublin University of Technology (LUT) comprising modelling of composite materials and their applications to civil, mechanical and aircraft engineering. The major goal and novelty of the project is to link together nano-, micro-, meso- and macro-scales to get perfect description of the composite behaviour under different loadings, temperature and environmental conditions. The project implementation will result in creating a leading research and education centre in the Middle-East part of Europe in modern composite materials and their applications to construction elements. With regard to research, it is envisaged to develop modern approaches to engineering structures made of composite and smart materials using non-linear theory for static and dynamic loading, new concepts of control, optimisation of the structure and methods of experimental investigations and identification of models. With regard to education, it is planned to provide teaching at the European level, consistent with EC priorities - by introducing new courses to existing Ph.D. studies programme, arranging advanced courses for the LUT staff and training LUT staff at partner institutions. It is envisaged to strengthen co-operation with the local industry: Polish Aviation Work Swidnik S.A. , Wiz-Art Ltd, local SME and new company AERONET- Aeronautic Valley, promote new technologies of composites and structural elements production and foster innovation to the local enterprises. In terms of socio-economical aspects, ToK project will help Lublin area (where LUT is situated)- as less favoured region - to compensate disproportion.The proposed project will increase international competitiveness of LUT in the field of composite materials and their applications to engineering structures. Involvement of LUT in joint European research projects will be enhanced by increase of long term research and collaborative capacity of LUT with EU institutions.

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Viele Materialien oder Medien in der Natur und Technik besitzen eine Mikrostruktur, die das Makroverhalten entsprechend prägt. Oft und trotz eventueller Schwierigkeiten bei der Beschreibung der entsprechenden Topologie ist die Kenntnis der relevanten Mechanismen auf Mikrostrukturebene umfassender als auf der Makroebene. Andererseits sind aber nicht alle Informationen auf der Mikroebene für das Verhalten auf der Makroebene relevant. Deswegen werden Mitteilungs- oder Homogenisierungs-Methoden benötigt, um aus den Mikro-Informationen geziehlt diejenigen herauszufiltern, die das Makroverhalten bestimmen. Dies eröffnet geleichzeitig in vielen Fällen die Möglichkeit, Mikrostrukturen gezielt zu entwerfen oder zu beeinflussen, um die Makroeigenschaften von Werkstoffen zu optimieren.

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Für neue Kriechgleichungen sind in einem ersten Schritt die Materialparameter zu identifizieren. In einem zweiten Schritt sind die Gesetze in kommerzielle Software zu implementieren. Zur Verifikation der FE-Software werden spezielle benchmarks entwickelt.

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Phänomenologische Werkstoffgesetze sind in Ingenieuranwendungen bis heute dominant. Innerhalb des Projektes wurden unterschiedliche Konzepte miteinander verglichen und bezüglich ihrer Einsatzgrenzen überprüft.

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Der Trafo-Blechverbund wird als Balken im Sinne der Technischen Mechanik modelliert. Die klassischen Ansätze der elementaren Theorie genügen nicht, da mit großen Verformungen gerechnet werden muss. Daneben sind für das Problem die Randbedingungen sorgfältig einzuarbeiten.

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Bei der Bauteilsimulation nimmt eine zentrale Stellung das Werkstoffmodell ein. Im Rahmen des Projektes werden zwei Konzepte miteinander verglichen: das phänomenologische Modell, welches die Mikrostruktur weitestgehend unberücksichtigt lässt, und mikromechanisch basierte Modelle.

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Für die Bewertung von Implantaten, die Entwicklung neuer Biomaterialien und die gezielte Oberflächenmodifikation von Implantatwerkstoffen, die im Skelettsystem verankert werden sollen, ist die quantitative Untersuchung der Belastungsfähigkeit des Interface zwischen Implantat und Knochen von grundlegender Bedeutung. Zur Bewertung der Grenzflächeneigen-schaften hat sich die Untersuchung der Scherfestigkeit der Grenzfläche im Tiermodell bewährt, die von den meisten Experimentatoren im push-out-Test oder im pull-out-Test durchgeführt wird. Bisher wird aus diesen Prüfungen jedoch meist nur die erreichte Maximalkraft bzw. Scherfestigkeit ausgewertet. Das Versagen der Implantat-Knochen-Grenzfläche erfolgt jedoch lastabhängig durch konsekutives Abreißen der anhaftenden Knochenbälkchen, wobei Typ und Behandlung des Implantatmaterials und die Verweildauer im Organismus entsprechenden Einfluss ausüben. Um Informationen über das beginnende Versagen und die Schädi-gungskinetik zu erhalten, wurde der push-out-Test um die simultane Schallemissionsprüfung erweitert, mit der die aktuelle Schadensentwicklung verfolgt werden kann. Damit sind in der Anfangsphase des Kraft-Weg-Diagramms vor Erreichen der Maximalkraft die Scherkräfte messbar, bei denen erste Ablösungen des Implantates vom umgebenden Knochen auftreten. Das beginnende Grenzflächenversagen wird durch die kritische mechanische Energie beim Einsetzen der akustischen Emission bestimmt, wobei die parallel registrierten mechanischen Kenngrößen die Scherspannung und Deformation definieren. Beim Versagen eines Implantates z.B. der Lockerung eines künstlichen Gelenkes, kommt es in der Regel nicht zu einem abrupten Versagen der Grenzfläche zwischen Knochen und Implantat, sondern zu einem allmählichen, schrittweisen Grenzflächenversagen mit Nachsinken oder Lockerung der En-doprothese. Dieses partielle Debonding des Interface von Knochen und Implantat führt sekundär zu einer Überlastung des Knochengewebes an den verbliebenen Kontaktstellen, lokalen Lastspitzen und so zum Fortschreiten der Desintegration des Implantates mit makrosko-pisch feststellbarer und klinisch evidenter Lockerung.

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Das Projekt ist Bestandteil des Leonard-Euler-Studienprogramms 2005/2006. Es dient der Förderung des wissenschaftlichen Nachwuchses in der Ukraine. In das aktuelle Programm sind 2 ukrainische Studenten eingebunden, die eine 9monatige Förderung in der Ukraine und einen 1monatigen Aufenthalt in Deutschland erhalten. Thematisch sind zwei Arbeitsrichtungen integriert:Thema 1: Modellierung des Verhaltens eines KompositwerkstoffesThema 2: Modellierung einer Sandwichstruktur

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Für zahlreiche Bauteile für Hochtemperaturanwendungen ist die Lebensdauerabschätzung im Kriechbereich die wichtigste Aufgabe bei der Vorbereitung von Einsatzentscheidungen. Ziel dieser Arbeit ist es, einen umfassenden Überblick über die theoretische Modellierung und die Analyse des Kriechens und der Langzeitfestigkeit von Bauteilen zu geben. Dabei stehen folgende Schwerpunkte im Mittelpunkt: Konstitutivgleichungen für das Kriechen von Ingenieurwerkstoffen unter mehrachsigen Beanspruchungen, strukturmechanische Modelle für Balken, Platten, Schalen und dreidimensionale Körper sowie numerische Verfahren für die Lösung nichtlinearer Anfangs-Randwertaufgaben der Kriechmechanik. Im Rahmen der konstitutiven Modellierung werden zahlreiche Erweiterungen der Mises-Odqvist-Kriechtheorie wie die Einbeziehung der Art des Spannungszustandes, der Anisotropie sowie der Verfestigungs- und Schädigungsvorgänge diskutiert. Für Sonderfälle der Materialsymmetrien werden geeignete Invarianten des Spannungstensors, Ansätze für Vergleichsspannungen und -dehnungen sowie Konstitutivgleichungen zum anisotropen Kriechen formuliert. Das Primärkriechen und transiente Kriechvorgänge können durch die Einführung von Verfestigungsvariablen beschrieben werden. Die Modelle der Zeit- und Deformations- sowie der kinematischen Verfestigung werden bezüglich der Vorhersagbarkeit des mehrachsigen Kriechens, die bisher auf die Beschreibung des Tertiärkriechens und der Langzeitfestigkeit angewandt wurden. Für einige Ingenieurwerkstoffe werden Kriechkurven, Konstitutivgleichungen, konstitutive Funktionen und Werkstoffkennwerte anhand der in der Literatur publizierten Daten zusammengefasst. Ferner wird ein neues Modell zur Beschreibung des anisotropen Kriechens in einem mehrlagigen Schweißgut vorgestellt.Die Grundgleichungen für das Kriechen in dreidimensionalen Körpern werden zum Zweck der Formulierung von Anfangs-Randwertproblemen, Variationsverfahren und Zeitschrittalgorithmen zusammengefasst. Zahlreiche Modelle der Strukturmechanik für Balken, Platten und Schalen werden bezüglich ihrer Anwendbarkeit auf Kriechprobleme diskutiert. Hier wird auf Effekte wie Querschubverzerrung, Randschichten und geometrische Nichtlineatitäten aufmerksam gemacht. Modelle mit Schädigungsvariablen werden mit Hilfe einer benutzerdefinierten subroutine in das Programmsystem ANSYS eingebunden. Für deren Verifikation werden Testaufgaben entwickelt und mit Hilfe spezieller numerischer Verfahren gelöst. Berechnungen der selben Aufgaben mit der Methode der finiten Elemente illustrieren die Anwendbarkeit der entwickelten subroutine für verschiedene Typen von finiten Elementen. Weiterhin zeigen sie den Einfluss der Netzdichte auf die Lösungsgenauigkeit. Abschließend wird die Langzeitfestigkeitsanalyse einer räumlichen Rohrleitung vorgestellt. Die Ergebnisse zeigen, dass das entwickelte Verfahren in der Lage ist, die wesentlichen Kriech- und Schädigungsvorgänge in Ingenieurkonstruktionen darzustellen.

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Endlosfaserverstärkte Thermoplastwerkstoffe zeigen ein von der Belastungs- oder Dehngeschwindigkeit abhängiges Materialverhalten. Um dieses Materialverhalten zu modellieren, werden die Materialkennwerte als zeitabhängig betrachtet und in einem linearen viskoelastischen Materialgesetz in Integralformulierung angewendet. Durch die Konzentration auf unidirektional endlosfaserverstärkte Thermoplastwerkstoffe vereinfacht sich das Materialgesetz in eine Formulierung für transversal isotrope Werkstoffe. Dieses Konstitutivgesetz für transversal isotrope Werkstoffe wurde in das Finite-Elemente-Programm ABAQUS implementiert. Für einachsige Beanspruchungen lässt sich die analytische Lösung mit der Simulation vergleichen. Zur Validierung des Materialmodells ist es notwendig Versuche an einfachen Probengeometrien durchzuführen und die Ergebnisse mit den Resultaten der Simulation zu vergleichen. Dabei ist der mögliche Anwendungsbereich auszutesten und entsprechende Materialparameter zu bestimmen. Im Anschluss an diese Untersuchungen können komplexere Bauteile berechnet werden.

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Viele Materialien oder Medien in der Natur und Technik besitzen eine Mikrostruktur, die das Makroverhalten entsprechend prägt. Oft und trotz eventueller Schwierigkeiten bei der Beschreibung der entsprechenden Topologie ist die Kenntnis der relevanten Mechanismen auf Mikrostrukturebene umfassender als auf der Makroebene. Andererseits sind aber nicht alle Informationen auf der Mikroebene für das Verhalten auf der Makroebene relevant. Deswegen werden Mitteilungs- oder Homogenisierungs-Methoden benötigt, um aus den Mikro-Informationen geziehlt diejenigen herauszufiltern, die das Makroverhalten bestimmen. Dies eröffnet geleichzeitig in vielen Fällen die Möglichkeit, Mikrostrukturen gezielt zu entwerfen oder zu beeinflussen, um die Makroeigenschaften von Werkstoffen zu optimieren.

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Durch eine vergleichende Analyse wurde die Umstellung des Studiums entsprechend dses Bologna-Prozesses in drei Ländern für den Maschinenbau betrachtet. Dabei traten Gemeinsamkeiten, aber auch deutliche Unterschiede in den einzelnen Ländern hervor. Dies betrifft Studienbschlüsse und Studienzeiten. Die Analage des Promotionsstudiums war dagegen nahezu identisch.

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Untersuchung von dünnwandigen Strukturmodellen auf der Grundlage klassischer und verbesserter Ansätze zur Kinematik bzw. zum Spannungszustand. Modelle der Kriechmechanik unter Einbeziehung nichtklassischer Effekte des Materialverhaltens. Einbeziehung der Schädigung in kriechmechanische Analysen. Einsatz kommerzieller Finite-Elemente-Programme bei Aufgaben der Strukturmechanik unter Berücksichtigung inelastischen Materialverhaltens. Berechnung herstellungstechnologisch bedingter Spannungen und Verzerrungen in Bauteilen aus verstärkten Kunststoffen.

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Zahlreiche dünnwandige Bauteile lassen sich als Schalen oder Platten modellieren. Basierend auf numerischen Lösungen von Anfangs-Randwertproblemen für die mathematische Modellierung der Kriechschädigung in Strukturelementen werden phänomenologische Materialmodelle zur Beschreibung von Werkstoffkriechen und Schädigung verglichen und bewertet, wobei eine Beschränkung auf stationäre Beanspruchungs- und Temperaturbedingungen erfolgt. Die Parameter der Materialmodelle werden an die aus der Literatur bekannten experimentelle Daten zum Kriechen metallischer Werkstoffe angepaßt. Die in der Kirchhoff-Love-Theorie getroffenen Annahmen sind bei zeitabhängigem Materialverhalten in Platten und Schalen nicht immer erfüllt. Im Vergleich zu den bisherigen Arbeiten wird daher eine verbesserte Schalenkinematik mit unabhängigen Rotationen eingesetzt. Die Modelle werden in verfügbare Rechenprogramme (spezielle Eigenentwicklungen, FE-Systeme) zum Zweck der Verallgemeinerung bei komplexer Geometrie übertragen und verifiziert.

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Entwicklung von Modellvorstellungen und konstitutiven Gleichungen zur Beschreibung des uinneren Zustandes und der Schädigung des Materials. Entwicklung von finiten Elementen für die dünnwandigen Verbundstrukturen unter Berücksichtigung nichtmechanischer Effekte. Optimae Auslegung von geregelten Leitbaustrukturen unter Nutzung von Parallelrechnern. Iterative Modellanpassungsverfahren für große FEM-Modelle realer Strukuren mit Hilfe experimenteller Daten mit Parameterschätzverfahren unter Einfluß stochastischer Größen

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