supervised students

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1. Exploration of the Third Dimension in the Design of Mechanical Metamaterials

   Azad Sahin Topcu

   Bachelor's Thesis Leibniz Universität Hannover, in progress
2. Machine Learning-Aided Inverse Design and Optimization of Porous Metamaterials

   Haoning Wang

   Doctoral Thesis Leibniz Universität Hannover, in progress
3. Patient Specific Implant Design and Surgical Planning through Machine Learning-Aided Design

   Badr Eddine Ayouch

   Doctoral Thesis Leibniz Universität Hannover, in progress

2024

1. Multiscale Modelling of Lattice Materials A novel approach using Beam Neural Networks

   Paul van IJzendoorn

   Master's Thesis Technische Universiteit Delft, 29. Nov 2024

   Abs URL

   A novel surrogate model to approximate microscopic behaviour and accelerate concurrent multiscale finite element simulations is proposed. The study serves as a proof of concept, focusing exclusively on 2D, geometric non-linear lattice materials. Despite numerous successful implementations of surrogate modelling techniques in literature, challenges remain, mainly with the black-box nature of most of these models, suffering from lack of interpretability. To tackle these issues, this study reintroduces physics into the model through the use of beam theory in so-called Beam Neural Networks. These networks are tested against a benchmark feed-forward neural network in both interpolation and extrapolation. Although the findings do not satisfy the requirements for practical application, they do indicate that the introduction of beam theory to the model has improved the model’s extrapolation ability, suggesting that the proposal has improved robustness and interpretability of the model. Given further optimization, there is promise of Beam Neural Networks to become an useful tool to accelerate concurrent multiscale modelling in the future.

2. Stiffness of Architected Materials

   Joris Smit

   Bachelor's Thesis Technische Universiteit Delft, 24. Jun 2024

   Abs

   This report investigates the linear-elastic response of the specific architected material called the arrowhead. Architected materials, are materials that show customized behavior in material properties and geometry. The material properties in architected materials are changed by the shape and design, rather than by changing the chemical composition of the material. The design of the arrowhead in this report is connected into the third dimension at two angles. These connection angles are 60° and 90°, and lead to two structures with different material properties. The goal of the report is to find how the elastic properties of these structures vary in response to loading along different directions in the linear regime. First the responses of the arrowhead design in two dimensions are investigated. The relationship between strain and stress is determined by formulating a stiffness matrix. Together with a rotation matrix the responses to loading along all angles can be calculated. Afterwards the theory is expanded to the third dimension, and the responses of the two different connection angles are calculated. The 60° connection angle structure showed less variance in its response to different directions of the investigated strains. Further did this structure exhibite higher normal stresses as a response to the investigated strain, indicating a greater resistance against deformations. The 90° connection angle structure showed more variance in the stress response at different loading directions. Overall, this structure did have lower values for the responding stresses to the investigated strains. The different structural angles also show similarities in the rotation angles at which the resistance was highest for the investigated strains. The optimal angle for the structures depends on the stresses acting on the material and the necessary requirements it must meet in engineering applications. In this report is assumed that all the responses of the material are linear-elastic. This results in small errors for small deformations, but significant errors if the deformations get bigger.

3. Finite Element Analysis of Structures Comparing Large and Small-Scale Structures in Linear and Non-linear Behaviour

   Amine Alami

   Bachelor's Thesis Technische Universiteit Delft, 25. Jun 2024

   Abs URL

   The use of computers in engineering started in 1960. Before 1960, engineers used physical models to check the results of complex structures. Recently, these physical models have been used for education purposes, namely, in the minor Bend and Break. Conversion from small-scale structures to real-sized structures was taught in this minor (P. C. J. Hoogenboom, n.d.). Therefore, This research aims to find a relation between small-scale and real-sized structures. Namely, the conversion of internal forces and displacements from a small-scale structure to a real-sized structure in both linear and non-linear material behaviour. A linear calculation yields a linear relation between the results and the applied force on the structure, unlike a non-linear calculation. The conversion rules apply to linear material behaviour. However, whether they also apply to physical and geometrical non-linear material behaviour is uncertain. This uncertainty yields the following research question: “There are conversion rules for deflection and stresses from small-scale structures to real-sized structures. Do these apply to non-linear behaviour too?” Multiple structures were analysed. A small-scale and real-sized model of these structures was modelled in the finite element program SCIA Engineer (SCIA, 2024). The geometrical properties of the smallscale structures were 10 times smaller than the geometrical properties of the real-sized structures. The type of structures is itemized below: • A steel truss (with and without bending stiffness) • A steel beam (statically determinate and statically indeterminate) • A steel Vierendeel girder • A concrete two-way slab • A concrete shell roof Geometrical and physical non-linear calculations were done. The geometrical non-linearity focused on local and global buckling, which yields large displacements while physical non-linearity focused on the plasticity of hinges and elastoplastic stress-strain diagrams. Relevant forces in the structures’ members and nodes were computed with linear and non-linear calculations. Additionally, displacement and deformations of relevant members or nodes were analysed. Furthermore, the applied loads are point loads, line loads or distributed loads, which had their conversion rules from small-scale to real-sized structures. Namely, the real-sized point load is 100 times larger than the small-scale point load. The real-sized line load is 10 times larger than the small-scale line load and distributed loads are identical in both structures. This yields identical stresses in the small-scale and real-sized structures. Displacements differ by a factor of 10 and internal forces by a factor of 100 or 1000, depending on the type of applied load. The steel trusses, the statically determinate beam, the Vierendeel girder and the concrete shell roof were all analysed with a geometrical non-linear calculation. All linear analyses followed the conversion rules perfectly. The relevant displacements in the small-scale structures differed by a factor of 10 from the displacements in the real-sized structures. The internal forces differed by a factor of 100 or 1000. Similarly, in the geometrical non-linear calculation, the displacements differed by a factor of 10 and the internal forces by a factor of 100 or 1000. However, there were small numerical errors in the nonlinear calculation. This happens when SCIA Engineer makes a non-linear calculation due to its iterative calculation method. The statically indeterminate beam and the concrete two-way slab were analysed with a physical non-linear calculation in addition to geometrical non-linearity. The plasticity of hinges was tested in the statically indeterminate beam and the elastic stress-strain curve of the two-way slab model was changed to an elastoplastic stress-strain curve which yields large displacements. Again, the internal forces differed by a factor of 100 or 1000, depending on the type of applied load. The displacements differed by a factor of 10, which is in line with the existing conversion rules. In conclusion, for the analysed structures, the conversion rules apply to both geometrical and physical non-linear material behaviour.

2022

1. GNNs and Beam Dynamics Investigation into the application of Graph Neural Networks to predict the dynamic behaviour of lattice beams

   Alexander Niessen

   Master's Thesis Technische Universiteit Delft, 12. Dec 2022

   Abs URL

   In the past decade, the application of Neural Networks (NNs) has received increasing interest due to the growth in computing power. In the field of computational mechanics, this has led to numerous publications presenting surrogate models to assist or replace conventional simulation methods. A subset of these networks, referred to as Graph Neural Networks (GNNs) impose the graph-like structure of many physical problems as a relational inductive bias. Several time-stepper implementations of these GNNs are reported to be able to simulate the dynamic behaviour of various physical objects. Within this work, it is investigated whether such GNN-based surrogate models can be applied to simulate the dynamic behaviour of lattice structures. Upon inference of such a GNN surrogate model, the computational time required for studying lattice behaviour could be considerably reduced, thus advancing research into lattice structures as metamaterials. In addition, many large-scale structures also form a composition of beams, which could be modelled with a similar GNN. To this end the following research question was defined: ”To what extent can GNNs be applied to simulate the dynamic behaviour of lattice structures using time-stepper methods?”. To answer this question, several GNN architectures were constructed and subsequently analyzed. In this research, it was found that the complexity of lattice structures could not be modelled in such a way as to obtain reliable, generalisable and stable behaviour, using a time-stepper method with an architecture similar to that of Pfaff et al., 2020. It was found that due to the existence of three physically different coupled Degrees of Freedom (DOF) per node the behaviour was too complex to learn for the proposed surrogate. At the time of writing, there is no publication presenting an effective surrogate model to simulate the dynamic behaviour of a Timoshenko beam using time-stepper methods. It is concluded that the need to capture both bending and shear behaviour using a Timoshenko beam formulation is the bottleneck for successfully modelling lattice structures.