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. However, the topics are not necessarily fixed but can be adapted to your interests/preferences if necessary. 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 convenience, all papers can alternatively be written in English.
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Bloch waves for structural analysis and 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, for example for acoustic waves, the determination of effective material properties or instability analysis. For natural materials such as bones, microstructures in steel as well as for artificial designs, the fact that elementary cells have a periodic structure is often exploited. 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. preparation of 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 - metallic crystals, biological structures or artificial fractals are possible, for example.
Contact: Dr.-Ing. Patrick Kurzeja
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Implementation and analysis of an element-erosion model for the modeling of brittle cracking (M.Sc. thesis)
Implementation and analysis of an element-erosion model for the modeling of brittle cracking (M.Sc. thesis)The formation and propagation of cracks in structural elements is of great importance for engineering, as the damage can lead to a considerable reduction in load-bearing capacity and even to the failure of structural elements. The simulation of brittle fractures is numerically demanding due to the unstable material behavior and the discontinuous material distribution and is the subject of current research work. 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 is to be implemented as described in [1] and its performance is to be examined using selected benchmark tests.
Contact: Felix Rörentrop, M. Sc.
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Strain gradient vs. damage gradient (Project thesis, B.Sc. thesis)
Strain gradient vs. damage gradient (Project thesis, B.Sc. thesis)When modelling softening materials with the finite element method, so-called localization occurs. Softening only affects 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 today. One widely used option is to include additional gradients in the model. Both the gradient of damage [1] and the gradient of equivalent distortion [2] can be used for this purpose. In this work, an existing local 1D damage model is to be extended by both approaches. The advantages and disadvantages will then be demonstrated 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. 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 the augmented Lagrangian approach (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 crystalline lattice structure at the micro level of materials and thus enable predictions about textures and material properties in forming processes. Rate-independent models have an ambiguity in the slip systems. There are numerous approaches in the literature to tackle the problem on the numerical side. On the other hand, a well-defined and physically motivated algorithm can be developed with the extended Lagrange function [1]. The aim of the thesis is to implement this algorithm in the context of the finite element method and to investigate representative examples, such as tensile tests or deep drawing processes. Since the crystal plasticity models are very computationally intensive, an efficient implementation using the C++ based deal.II FEM library is aimed for [2]. In addition to the use of different element types or mesh refinement strategies, parallelization on up to 16,000 processors is also possible.
[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 optimization routine (M.Sc. thesis)
One of the main benefits of simulations is the algorithmic optimization 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 optimize alread existing designes 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
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Development of a physically well-motivated material model for rate-independent crystal plasticity (M.Sc. project work, M.Sc. thesis)
Development of a physically well-motivated material model for rate-independent crystal plasticity (M.Sc. project thesis, M.Sc. thesis)Material models for the simulation of rate-independent crystal plasticity considering finite deformations have existed for quite a long time and are well established. Nevertheless, these models have 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 slip occurs there. Although the stresses result correctly, the active slip systems and their conductions are almost arbitrary. This would in any case lead to major problems if, for example, phenomena such as "cross hardening" (also known as "latent hardening") are to be taken into account. The aim of this work is to enrich the classical crystal plasticity models with additional and physically motivated considerations in order to circumvent the problems described above.
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 model size effects due to the lack of a natural length scale. Although these effects can generally be neglected on the macroscale, experimental and theoretical investigations suggest that they become significant as the length scale decreases. In the context of this work, an introduction to an extended continuum theory with special reference to fiber-reinforced materials will first be given, see [1]. This is based on the extension of the energy function by contributions that take into account higher gradients of the displacement field energetically and requires higher continuity requirements for the intended solution using the finite element method. Against this background, finite elements with additional rotational degrees of freedom are to be implemented and used to investigate representative boundary value problems, see [2] and [3].
Literature:
[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, 483-487Contact: PD Dr.-Ing. habil. Tobias Kaiser
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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 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 computing time and at the same time make efficient use of the working memory. With "reduced integration", however, standard elements do not behave as desired, as so-called "zero-energy modes" (hourglassing) occur. The resulting finite element solution is therefore unusable. In the context of this work, elements are to be implemented in the institute's own MATLAB code that utilize "reduced integration" and at the same time suppress the occurrence of hourglassing. The behavior of the element formulation will also be investigated with the help 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 used in the context of 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 via 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 do justice to its significance as a volume fraction, namely 0 <= p <= 1. These conditions are enforced via restricted optimization methods, e.g. via penalty or (augmented) Lagrangian methods as standard. This thesis will now examine the extent to which the so-called interior point algorithm is suitable for this purpose. In addition to the theoretical consideration, this naturally also includes an implementation of the whole thing.Contact: Hendrik Wilbuer, M.Sc.
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Characterization of material classes based on machine learning (B.Sc. thesis, M.Sc. thesis)
Characterization of material classes based on machine learning (B.Sc. thesis, M.Sc. thesis)Aspects of sustainability and environmental protection are becoming increasingly important in the design process. The development of resource-saving products, which at the same time must be cost-effective and have the required strength, represents a complex optimization task. An important part of this process is the selection of materials. Nowadays, countless different materials with a wide range of properties are available. The aim of this work is the characterization of material properties, e.g. stiffness, for different material classes based on parameters of the microstructure, e.g. porosity. This not only allows the designer a quick overview of certain properties of the material classes, but also facilitates the design of new, optimal materials for the desired application. The latter is (more easily) possible nowadays, particularly thanks to new technologies such as 3D printing.
In this thesis, the relationships between the material properties and the selected parameters are to be investigated using symbolic regression. Symbolic regression is a branch of machine learning. It searches for a function as a combination of basic mathematical blocks that best fits a given data set. A major advantage of the method is the interpretability of the functional correlation of the data.
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Simulations of elastic material behavior based on artificial intelligence (B.Sc. thesis, M.Sc. thesis)
Simulations of elastic material behavior based on artificial intelligence (B.Sc. thesis, M.Sc. thesis)Aspects of sustainability and environmental protection are becoming increasingly important in the design process. The development of resource-saving products, which at the same time must be cost-effective and have the required strength, represents a complex optimization task. Nowadays, simulations are indispensable for reducing the number of experiments during this development process. However, classic FEM simulations quickly reach their limits for industrial components and complex material behavior. Especially with regard to the computing time, which must be kept as short as possible in industrial applications. In this context, models from the field of artificial intelligence, e.g. neural networks, promise a flexible and efficient solution. Therefore, a new class of neural networks for the prediction of elastic material behavior will be implemented in this thesis. Subsequently, the quality of this method will be investigated and evaluated using different criteria.
Contact: Gian-Luca Geuken, M.Sc.
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Weiterentwicklung eines Materialmodells für die Festkörperphasenumwandlung bei großen Verformungen - Anwendung auf Laser-Pulverbettfusion Prozesse (M.Sc. Arbeit)
Development of a large strain solid state phase transformation model - application to laser powder bed fusion processes (M.Sc. Thesis)Laser powder bed fusion (L-PBF) is a cutting-edge additive manufacturing (AM) techniques enabling the layer-wise production of components by selectively melting metallic particles with a laser beam. This thesis aims to enhance the understanding and prediction of warpage and residual stresses in L-PBF by developing a large strain solid state phase transformation model based on [1]. Thereby, the focus is set on dual phase materials like Ti6Al4V. The model parameters shall be fit using continuous cooling transformation (CCT) diagrams, where an appropriate parameter identification (PI) algorithm has to be implemented to determine optimal model parameters. The ultimate goal is to integrate this model into the commercial simulation software Abaqus to improve the simulation accuracy in terms of warpage and residual stresses. With this, the different solid phases can be predicted and an inherent strain tensor can be determined necessary for the multiscale framework used in, e.g., [2].
[1] Noll, I., Bartel, T., & Menzel, A., A thermodynamically consistent phase transformation model for multiphase alloys: application to Ti6Al4V in laser powder bed fusion processes, Computational Mechanics, available online, 2024
[2] Noll, I., Koppka, L., Bartel, T., & Menzel, A., A micromechanically motivated multiscale approach for residual distortion in laser powder bed fusion processes, Additive Manufacturing, 60(Part B), 103277, 2022
Contact: Dr.-Ing. Isabelle Noll -
Modellierung der Gasphase in additiven Fertigungsprozessen (B.Sc. Arbeit, Projekt Arbeit, M.Sc. Arbeit)
Vapor phase modeling in additive manufacturing (B.Sc. Thesis, Project thesis, M.Sc. Thesis)
Laser powder bed fusion (L-PBF) is a cutting-edge additive manufacturing (AM) techniques enabling the layer-wise production of components by selectively melting metallic particles with a laser beam. In this thesis, a simplified material model based on [1] shall be extended through an additional vapor phase to better understand process defects like porosity. First, a literature search on various vapor phase modelling approaches in L-PBF has to be conducted. The objective of this theses is to determine the most suitable vapor phase model and incorporate it into the existing material model. Subsequently, the modified material model will be used to simulate a single melt line using the commercial simulation software Abaqus. The goal is to enhance the understanding of vapor phases by giving insight into the the different states during the process, i.e. powder, melt, vapor and solid, and improve the simulation accuracy.
[1] Noll, I., Bartel, T., & Menzel, A., A computational phase transformation model for Selective Laser Melting processes, Computational Mechanics, 66, 1321-1342, 2020
Contact: Dr.-Ing. Isabelle Noll -
Weiterentwicklung der inhärenten Dehnungsmethode für Laser-Pulverbettfusion-Prozesse (B.Sc. Arbeit, Projekt Arbeit, M.Sc. Arbeit)
Advancing the inherent strain method used for laser powder bed fusion processes (B.Sc. Thesis, Project thesis, M.Sc. Thesis)
Laser powder bed fusion (L-PBF) is a cutting-edge additive manufacturing (AM) techniques enabling the layer-wise production of components by selectively melting metallic particles with a laser beam. The inherent strain method is applied to generate simulation results of complete parts computationally efficient. First, different inherent strain methods found in literature shall be compared, analyzing their advantages and disadvantages. The new material model shall be applied to more complex boundary value problems simulated with help of the commercial simulation software Abaqus, including a bridge, an L-shaped part with a hole and the NIST AM benchmark. Depending on the thesis type, inherent strains will either be predefined or calculated independently. The goal of this thesis is to incorporate plasticity into the material model used for the multiscale framework in [1] for more accurate simulation results.
[1] Noll, I., Koppka, L., Bartel, T., & Menzel, A., A micromechanically motivated multiscale approach for residual distortion in laser powder bed fusion processes, Additive Manufacturing, 60(Part B), 103277, 2022
Contact: Dr.-Ing. Isabelle Noll