Cables, slender structural elements, are ubiquitous in engineering structures. Their applications span diverse fields, including bridges, ski lifts, and tensile architecture, as well as electrical conduction and signal transmission. This multifaceted use results in a wide range of configurations and performance demands. Cable cross-sections typically comprise multiple materials, including insulating and protective rubber layers, conductive copper or other metals, and potentially reinforcing woven fibers for electrical shielding or structural enhancement. The complex interplay between these components, particularly frictional contact over large interfacial areas, poses significant numerical challenges and demands substantial computational resources. The finite element method [1] is a highly versatile approach well-suited for such complex nonlinear computations. To mitigate these complexities, a macroscopic material model can be employed, representing the cable as a homogeneous anisotropic material. This approach, while sacrificing geometric details, can reduce computational cost by capturing hyperelastic and elastoplastic behaviors at the macroscopic level. An example of a finite element computation of a coaxial cable together with a comparison with experimental data is shown in Figure 1, see also [6].

The aim of this master thesis is to develop a finite element simulation approach for coaxial cables using the Abaqus finite element software package [7]. Experimental data from a previous project [2-6] can be used for model validation. The developed solid finite element model should be capable of simulating tension, torsion, and bending tests, including cable-to-solid and cable-to-cabel contact. To achieve this, a suitable material model from the Abaqus library has to be selected, and its parameters determined based on existing experimental data. Additionally, different cross-sectional subdivision approaches shall be investigated to simplify the representation of the cable's complex geometry. The finite element model shall be numerically analyzed and validated against experimental results.

Contact

This master thesis will be jointly supervised by TUHH and Miele. For more information on this topic please contact

Prof. Dr.-Ing. habil. Alexander Düster, Numerical Structural Analysis with Application in Ship Technology, Institute for Ship Structural Design and Analysis, TUHH, alexander.duester@tuhh.de
or
Tom Rudolph, Miele, Division Smart Home Electronic, Miele & Cie. KG | Carl-Miele-Straße 29 | 33332 Gütersloh | Germany, tom.rudolph@miele.com

Recommended skills: Finite Element Method, Nonlinear Structural Analysis

Literature

[1] P. Wriggers, Nonlinear Finite Methods, Springer, 2008.
[2] A. Hildebrandt, A. Düster. Numerical Investigation of High-Order Solid Finite Elements for Anisotropic Finite Strain Problems. International Journal of Computational Methods, 19(5):2250007, 2022.
[3] A. Hildebrandt, P. Sharma, A. Düster, S. Diebels. Experimental and numerical investigation of the deformation behaviour of cables and thin beam-like structures under multi-axial loading. Mathematics and Mechanics of Solids, doi.org/10.1177/10812865221114299, 2022.
[4] P. Sharma, A. Hildebrandt, A. Düster, S. Diebels. Mechanical Characterisation of Cables in Different Loading Directions. Proceedings in Applied Mathematics and Mechanics, 22:e202200178, 2023.
[5] A. Hildebrandt, P. Sharma, S. Diebels, A. Düster. Efficient simulation of cables with anisotropic high-order solid finite elements. Proceedings in Applied Mathematics and Mechanics, 22:e202200168, 2023.
[6] A. Hildebrandt, P. Sharma, S. Diebels, A. Düster. Nonlinear computation of cables with high order solid elements using an anisotropic material model. Proceedings in Applied Mathematics and Mechanics, 20:e202000217, 2021.
[7] Dassault Systèmes: Abaqus 2021 Documentation (2021). www.3ds.com/products-services/simulia/products/abaqus/

The simulation of blood flow (hemodynamics) requires the simulation of a fluid-structure interaction problem such that it is very possible for this biomedical application to join forces with the simulation of flexible marine structures.
One of the main applications for blood flow simulations is the optimization of implants like stents, bypass-grafts or stent-grafts as well as external cardiovascular devices.
In recent years, we have developed a simulation approach that allows for investigations, e.g. of the hemodynamic in the connection by arteries and bypass-grafts, so-called anastomoses, as shown in the Figure.

In order to solve the coupled fluid-structure interaction problem, we reuse existing software for the structure and the fluid subproblem and couple them using a third software, our coupling manager comana.
In such a partitioned solution approach for coupled problems, the so-called added mass effect can lead to instabilities in the simulations. In biomedical applications, where the density of the fluid and the structure are almost equal this effect is especially problematic (as opposed to engineering applications considering, e.g. steel and water). While we can achieve stable simulations with novel stabilization methods from literature, we constantly work on improving and fine-tuning these. Theses focusing on these rather theoretical aspects may only perform larger simulations in an exemplary spirit and mainly work with academic test cases.

In an active research project, we currently use mathematical shape optimization methods in combination with the coupled simulation approach. Using the so-called adjoint method, our goal is to find optimal shapes. e.g. for anastomoses, that minimize or maximize clinically relevant hemodynamic factors associated, e.g. with the development of atherosclerosis or hemolysis.

Interested applicants are asked to contact:

Dr.-Ing. Lars Radtke, Prof. Alexander Düster

Presence of granular material in the cavity of a ship’s double hull leads to improved crashworthiness. Expanded glass granules (Poraver) have been found to be particularly suitable due to their chemical and physical properties. However, the abrasive behaviour of Poraver particles under dynamic load is a disadvantage for the application investigated. One way to overcome these problems is to use coated
particles.

The project involves the numerical modelling of coated particles, to be used in the cavitiy of a ship double hull to improve its crashworthiness, using the Discrete Element Method (DEM). The difficulty lies in the correct determination of large number of structural and material parameters for the numerical model. Furthermore, the simulation times are large especially when performing multi particle simulations as is the case when simulating a double hull. For this purpose, an open source code MUSEN is used. The validated numerical model will be used to simulate a collision scenario with a particle filled double hull to determine the extent of kinetic energy absorbing capabilities of coated particles.

Experimental studies consistently demonstrate that as the size of specimens increases, their fatigue strength tends to decrease. This phenomenon, often referred to as the thickness effect or size effect, is observed in both machined and welded specimens. While the exact mechanisms behind this phenomenon are not fully understood, various industry codes have acknowledged and accounted for the reduction in fatigue strength associated with increasing structure or component size. Typically, these codes incorporate a thickness correction factor to adjust for this effect, thereby scaling down the predicted fatigue strength in design and analysis processes. In contrast, stress gradients-based fatigue assessment methods are capable of directly accounting for geometric size effects; however, there has not been a thorough investigation on thickness effects on welded joints using such methods. Hence, this project is concerned with the application of different stress gradient-based methods such as the critical distance and stress averaging methods for welded joints of varying plate thickness. For this purpose, numerical simulations will be applied.

It is well known that the fatigue strength of notched components cannot be determined solely by calculating the stress peak σ_max at the notch tip by the theory of elasticity and using the fatigue strength or endurance limit ∆σ_R derived from unnotched specimens.^[1] In order to overcome this problem, a variety of different methods have been suggested, which take the stress gradient or so-called notch effect in the vicinity of a local stress raiser into account.

In recent years, attempts have been made to simplify these approaches and to find a method that is most suitable for fatigue assessment based on numerical simulations. Although, differences between the different approaches have been proven, it is generally assumed that some methods are directly comparable. Hence, this project is concerned with the investigation of the comparability of stress gradient or effective notch stress methods for fatigue assessment. For this purpose, numerical simulations will be applied in combination with metamodeling. The goal is to create surrogates based on non-linear curve fitting and machine learning in order to reduce computational efforts.

[1] A. Thum und W. Buchmann, Dauerfestigkeit und Konstruktion, VDI-Verlag, Berlin, 1932

Fatigue behaviour of welded joints depends on a number of factors, such as local weld geometry, macro-geometric misalignment, loading type, etc. Due to the complexity of this topic, machine learning techniques offer a possibility to assess the mutual influence of these aspects. In this study, different machine learning techniques, i.e. decision tree, boosted trees, and artificial neural network are utilised to to predict fracture locations and fatigue life of welded joints.

It is well known that there is an inherent risk in load-carrying fillet welded joints for fatigue fracture from the weld root. This is usually avoided by large throat thicknesses, which reduced the nominal stress in the cross-section of the fillet weld. However, the reason for weld root failure is not only governed by throat thickness, but also by other parameters like loading type, leg length and so on. Assessment of the risk of root failure can be either empirically or numerically. For the later, different methods are permitted by industry standards and or are still under development.

In recent years, attempts have been made to simplify these approaches and to find a method that is most suitable for fatigue assessment based on finite element method. Although, differences between the different approaches have been proven, it is sometimes believed that some of the methods are directly comparable. However, recent studies found differences in the estimating whether cracks will initiate from the weld toe or root for different methods. Hence, this project is concerned with the investigation of weld toe or root transition for load-carrying cruciform joints. For this purpose, finite element simulations will be applied.

Additive manufacturing as a new production process offers great advantageous for certain applications compared to classical processes; however, additively manufactured components are known to have poor surface quality after production. These surfaces can contain defects, from which fatigue cracks can be initiated. Possibilities to improve the fatigue strength included post-production methods like heat treatment or hybrid production processes (e.g. machining of the surface). In current projects the fatigue behavior of 316L specimens produced by selective laser melting and wire and arc additive manufactured are investigated. Topics for project and master thesis include:

• Fatigue strength of welded 3D printed materials
• Fatigue strength of wire and arc additive manufactured (WAAM) materials
• Hybrid additive manufacturing

Fluid-structure interaction plays an important role, especially in marine applications, where the loads acting on possibly deformable structures are mainly determined by the fluid around them.
In the past, we have considered several applications, such as ships in sea waves in order to simulate the landing maneuver of service ships to an offshore wind turbine plant as shown in the figure below.
It also includes snapshots of simulations of flexible marine propellers and floating offshore wind turbine plants.

In all of these applications, the interaction of fluid and structure must be considered to predict the structural integrity or the performance accurately.
This leads to a coupled problem, where loads have to be transferred from the fluid subproblem to the structural subproblem and where displacements of the structure have to be sent in the other direction.
For both subproblems, dedicated solvers already exist. It is therefore desired to reuse existing software and modify it such that coupling can be realized between two solvers instead of developing a new code that can handle both problems simultaneously.

Accordingly, we pursue a partitioned approach to solve the coupled problem rather than a monolithic approach. Through a third software, a coupling manager, the data exchange between the fluid and the structural solver (and possibly between any number of solvers for a variety of different problem types) is managed. A major field of research in our group is the development of new coupling algorithms and so-called convergence acceleration schemes inside our coupling manager comana. You can find below a list of publications around these topics.

In your thesis, you may work more on the application side and participate in one of our research projects, e.g. the acoustic behavior of flexible marine propellers or the simulation of a wave energy converter. Alternatively, topics which are less related to applications (e.g. about coupling algorithms and novel discretization schemes) are available.

Interested applicants are asked to contact:

Dr.-Ing. Lars Radtke, Prof. Alexander Düster

The main purpose of this project is to support the experiments of [2, 1] by modeling the dynamic response of ice. The motivation for this is twofold: understanding the dynamic behavior of ice can help us get insights into glacier dynamics, and it can help us better design ship structures.
An example from [2, 1] experiments of an ice cylinder impacted by a moving plate can be seen in the Figure.

Figure 1: Cracking stages of an ice cylinder impacted by a moving plate.

In this project the student will apply the phase-field approach [3] to model the dynamic cracking in an ice cylinder subjected to impact loading. In their experiments [2, 1] found that ice behavior is strain rate depended, starting with some ductility at small strain rates and tending to brittle behavior at high strain rates. Here, we will try to account to the entire range of the experimental strain rates directly through the variational formulation of the phase-field approach.

For further information contact us at:
Dr.-Ing. Yaron Schapira, schapira.y@gmail.com, yaron.schapira@tuhh.de, +972-54-5659884
Prof. Dr.-Ing. habil. Alexander Düster, alexander.duester@tuhh.de, 040-42878-6083

References
[1] Angelo Mario Böhm, Hauke Herrnring, and Franz von Bock und Polach. “Lessons Learned: The Influence of Testing Properties on Uniaxial Compression Tests of Ice”. In: International Conference on Offshore Mechanics and Arctic Engineering. American Society of Mechanical Engineers. 2022.
[2] Angelo Mario Böhm, Hauke Herrnring, and Franz von Bock und Polach. “Data from uniaxial compressive testing of laboratory-made granular ice”. In: Data in Brief 42 (2022), p. 108236.
[3] Yaron Schapira, Lars Radtke, Stefan Kollmannsberger, and Alexander Düster. “Performance of acceleration techniques for staggered phase-field solutions”. In: Computer Methods in Applied Mechanics and Engineering 410 (2023), p. 116029.

Sehr schnelle und/oder hochgradig nichtlineare Probleme der Festkörpermechanik werden mit Hilfe der expliziten Berechnungsmethoden gelöst. Anschauliche Beispiele solcher Berechnungen sind Crash- oder Umformsimulationen.
Momentan existieren auf dem Markt einige wenige Anbieter propriäterer Software, die explizite Solver entwickeln und vertreiben. Diese sind robust und validiert. Parallel dazu werden von der Open Source Community freie Alternativen entwickelt.
In dieser Arbeit soll eine vergleichende Untersuchung zwischen einem Vertreter der kommerziellen Software und Open Source auf Basis eine Umformsimulation erstellt werden. Als kommerzielle Software dient dem Projekt LS-DYNA und auf der Seite von Open Source OpenRadioss.

Vergleichende Untersuchung einer quasi-statischen Verformung mit LS-DYNA und OpenRadioss

In this project we are interested in studying and implementing an algorithm for simulating geometries with multiple parts using the FCM. The main objectives are: a) investigate and analyze existing algorithms and techniques for simulating complex geometries with multiple parts using FCM, b) implement the algorithm within a C++/Rust code, c) validate the developed algorithm by comparing the simulation results with experimental data or benchmark cases, demonstrating its accuracy and efficiency, d) evaluate the performance and scalability of the implemented algorithm in terms of computational efficiency, memory requirements, and robustness, e) provide documentation, user guidelines, and recommendations for future enhancements or extensions of the algorithm.

This thesis is in cooperation with Dr-Ing. Meysam Joulaian from SimScale GmbH.
For further information contact:

Finite element simulation of contact problems has become an indispensable tool in engineering analysis [1]. Contact constraints are typically enforced using Lagrange multipliers, penalty methods, or a combination of both approaches [2]. This thesis shall investigate a novel third medium contact formulation based on a space-filling mesh that enables contacting bodies to move and interact [3]. To accommodate contact constraints, the properties of the third medium embedding the bodies must adapt to their movements. The proposed approach employs an isotropic/anisotropic hyperelastic material model to represent the mechanical behaviour of the third medium. This eliminates the need for computationally expensive contact search algorithms and significantly simplifies the contact formulation. Preliminary results presented in [3] and independently computed using the high-order FEM code AdhoC [5] are encouraging (see Figure 1). The objective of this work is to study the third medium approach. The high-order finite element solver AdhoC will be employed to conduct comprehensive studies. These studies will assess the impact of the hyperelastic material model [1,3,4] on the convergence and stability of the contact algorithm, as well as the accuracy of the finite element solution in capturing the mechanical behavior of the system under contact conditions. The scope of the project will be tailored to the type of work (project or master thesis).

Recommended skills: Basic programming skills, finite elements

Literature
[1] P. Wriggers, Nonlinear Finite Methods, Springer, https://link.springer.com/book/10.1007/978-3-540-71001-1,2008.
[2] P. Wriggers, Computational Contact Mechanics, Springer, https://link.springer.com/book/10.1007/978-3-540-32609-0, 2006.
[3] P. Wriggers, J. Schröder, A. Schwarz, A finite element method for contact using a third medium, Computational Mechanics, 52:837-847, https://link.springer.com/article/10.1007/s00466-013-0848-5, 2013.
[4] J. Bonet, R.D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, https://doi.org/10.1017/CBO9780511755446, 2008.

[5] A. Düster, High-Order FEM, Lecture Notes, TU Hamburg, 2023.

[6] A. Düster, Nonlinear Structural Analysis, Lecture Notes, TU Hamburg, 2023.

Contact
For more information on this topic please contact