The topics listed below are suggestions for possible projects and are open to discussion. If you have another idea for such a project falling into the given fields, please do not hesitate to contact us. For the sake of simplicity, the titles and descriptions of the following projects are provided in German. Please note, that any thesis can be conducted in German or English.
The topics listed here are suggestions for possible projects that can be carried out in any case and documented in a corresponding student thesis. The topics are not necessarily fixed but can be adapted to your interests/preferences. If you have your own ideas for topics or if none of the topics listed here completely convince you, please do not hesitate to contact us. Please note that although the descriptions here are written in German for simplicity, all papers can alternatively be written in English.
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Bloch wave analysis for structural characterization (Project thesis, B.Sc. thesis, M.Sc. thesis)Bloch wave analysis for structural characterization (Project thesis, B.Sc. thesis, M.Sc. thesis)
Bloch functions are an important way to find periodic solutions in structures, e.g. for acoustic waves, determination of effective material properties or instability analysis. For natural materials like bones, microstructures in steel as well as for artificial designs it is often exploited that elementary cells have a periodic structure. This work pursues two goals, which can be weighted differently depending on the scope of the work: 1. development of a numerical solver for a reference cell, e.g. in Python or Matlab. 2. working up an example for a course. The system of investigation can be based on interest and field of study and is not limited to one discipline - possible examples include metallic crystals, biological structures, or artificial fractals.
Contact: Dr.-Ing. Patrick Kurzeja
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Implementationand analysis ofan element-erosion model for the modeling ofbrittle cracking (M.Sc.-thesis)Implementation and analysis of an element-erosion model for the modeling of brittle cracking (M.Sc.-thesis)
The initiation and propagation of cracks in structural elements is of great importance for engineering, since the damage can lead to a significant reduction of the load capacity up to the failure of structural elements. The simulation of brittle fractures is numerically challenging due to the unstable material behavior and discontinuous material distribution and is the subject of current research. The self-erosion approach considers elements as either intact or eroded (defective). The crack propagation is determined by considering the energy change during the erosion of the elements in a small area around the already defective elements. The model will be implemented as described in [1] and its performance will be investigated by means of selected benchmark tests.
Contact: Felix Rörentrop, M. Sc.
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Strain gradient vs. damage grad ient (Project thesis, B.Sc.-Thesis)
When modeling softening materials with the finite element method, the so-called localization occurs. The softening affects only one element series, so that the results depend on the size of this element series. In order to eliminate this localization behavior and to generate mesh-independent results, a variety of possibilities can be found in the literature nowadays. One widely used possibility is to include additional gradients in the model. For this purpose, both the gradient of damage [1] and the gradient of equivalent distortion [2] can be used. In this work, an existing local 1D damage model will be extended by both approaches. Then, the advantages and disadvantages will be shown using 1D and 2D examples.
[1] Dimitrijevic, B., & Hackl, K. (2008). A method for gradient enhancement of continuum damage models, Engineering Mechanics 1, 43-52. [2] Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M. and de Vree, J.H.P. (1996). Gradient enhanced damage for quasi-brittle materials, Int. J. Numer. Meth. Engng. 39, 3391-3403.
Contact: Kai Langenfeld, M.Sc.
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Efficient finite element implementation of a crystal plasticity model based on theaugmented Lagrangian function (B.Sc.-thesis, M.Sc.-thesis)Efficient finite element implementation of a crystal plasticity model based on the augmented Lagrangian approach (B.Sc.-thesis, M.Sc.-thesis)
Crystal plasticity models take into account the micro-scale crystalline lattice structure of materials and thus allow predictions of textures and material properties during forming processes. Rate-independent models possess ambiguity of the glide systems. Numerous approaches exist in the literature to address the problem on the numerical side. In contrast, a well-defined and physically motivated algorithm can be developed using the extended Lagrangian function [1]. The aim of this work is to implement this algorithm in the context of the finite element method and to study representative examples, such as tensile tests or deep drawing processes. Since crystal plasticity models are very computationally intensive, an efficient implementation using the C++ based deal.II FEM library is aimed at [2]. In addition to the use of different element types or mesh refinement strategies, parallelization on up to 16,000 processors is also possible, among other things.
[1] Schmidt-Baldassari, M. (2003). Numerical concepts for rate-independent single crystal plasticity, Comput. Methods Appl. Mech. Engrg., 192, p.1261-1280. [2] deal.II - an open source finite element library.
Contact: Alexander Niehüser, M.Sc.
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Implementation and validation of a shape optimisation routine (M.Sc. thesis)
One of the main benefits of simulations is the algorithmic optimisation of components without the need to design and produce several prototypes. In order to take full advantage of refined numerical material models, an automatic shape optimisation routine allows to optimise alread existing designs e.g. with respect to amount of material used, integral stiffness or some alternative requirements. Aim of this thesis is therefore the implementation of such a shape optimisation routine in c++ with an interface to an existing in-house FEM-code to solve the associated inverse problem.
Contact: Dr.-Ing. Lars Rose
- Material models for the simulation of rate-independent crystal plasticity considering finite deformations already exist for quite a long time and are well proven. Nevertheless, these models bring rather severe problems. More precisely, the solution of the problem becomes ambiguous as soon as more than a certain number of slip systems are activated in the underlying crystal, i.e. plastic sliding occurs there. The voltages result correctly, but the active glide systems as well as their glides are almost arbitrary. This would lead to big problems in any case, if e.g. phenomena like "cross hardening" (also called "latent hardening") should be considered. The aim of this work is to enrich the classical crystal plasticity models by additional and physically motivated considerations in order to be able to circumvent the described problem.
Contact: Dr.-Ing. Thorsten Bartel
- Implementation of finite elements with rotational degrees of freedom for the simulation of curvature effects in nanomaterials (M.Sc.-thesis)Implementation of finite elements with drilling degrees of freedom for the simulation of curvature effects in nanomaterials (M.Sc. thesis)
Classical continuum theories cannot represent size effects due to a missing natural length scale. Although these effects can be neglected on the macro scale, experimental and theoretical investigations suggest that they become significant with decreasing length scales. In the context of this work, we will first introduce an extended continuum theory with special reference to fiber-reinforced materials, see [1]. This is based on the extension of the energy function by contributions, which energetically considers higher gradients of the displacement field and implies higher continuity requirements for the intended solution by means of the finite element method. With this in mind, finite elements with additional rotational degrees of freedom will be implemented and used to study representative boundary value problems, see [2] and [3].
References: [1] Spencer, A. J. M. & Soldatos, K. P., Finite deformations of fiber-reinforced elastic solids with fiber bending stiffness, International Journal of Non-Linear Mechanics, Elsevier, 2007, 42, 355-368 [2] Ristinmaa, M. & Vecchi, M., Use of couple-stress theory in elasto-plasticity, Computer Methods in Applied Mechanics and Engineering, Elsevier, 1996, 136, 205-224 [3] Mohr, G., A simple rectangular membrane element including the drilling freedom, Computers & Structures, 1981, 13, 483-487
Contact: Tobias Kaiser, M.Sc.
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Implementation of reduced integration approaches in Abraxas++ (B.Sc. thesis)Implementation of reduced integration approaches in Abraxas++ (B.Sc. thesis)
The finite element method is one of the most common numerical methods in mechanical engineering today. However, many users know little about the underlying theory and rely on the robust implementation of the commercial finite element programs. Especially for very large models, elements with "reduced integration" are often used in practice in order to (among other things) save computation time and at the same time use the working memory efficiently. With "reduced integration", however, standard elements do not behave as desired, since so-called "zero-energy modes" (hourglassing) occur. The resulting finite element solution is thus unusable. In the context of this work, elements are to be implemented in the institute's own MATLAB code that exploit "reduced integration" and simultaneously suppress the occurrence of hourglassing. The behavior of the element formulation will furthermore be investigated by means of simulations.
Contact: Dr.-Ing. Thorsten Bartel
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Investigation of the interior-point method for application to phase-field models (project work, B.Sc. thesis, M.Sc. thesis).Investigation of the interior-point method for application to phase field models (Project thesis, B.Sc. thesis, M.Sc. thesis)
For the modeling of two-phase systems (generally also multiphase systems), so-called phase field models can be applied within the framework of the FEM. In addition to the mechanical analysis, these models use a variational approach to determine the most favorable phase at each point. This is implemented by an additional global field variable - the phase field p, which represents the volume fraction of the phases. The phase field parameter is subject to restrictions in order to meet the meaning as volume fraction, namely 0 <= p <= 1. These conditions are enforced by restrictive optimization methods, e.g. penalty or (augmented) Lagrangian methods. In the context of this work, it is now to be investigated to what extent the so-called Interior-Point-Algorithm is suitable for this purpose. This includes, besides the theoretical consideration, of course also an implementation of the whole thing.
Contact: Hendrik Wilbuer, M.Sc.