Establishing a framework for conducting comparative one- and multidimensional studies on the coupling of the finite element method with particle-based techniques
Creators: name: Laubert, Lukas
Publisher: name: Zenodo
Year: 2023
Subjects: Finite element method (FEM), Particle-based techniques, Capriccio method, Staggered scheme, Anchor points, Molecular dynamics (MD), Interdimensional comparability, Convergence behavior, Direct stiffness method, Periodic boundary conditions, Weighting scheme, Displacement measurement, Lagrange function

description: readme_projectThesis.txt <br> <strong>Description</strong>: This readme contains links to source codes, data, and supplemental materials of the<br> associated project thesis on this dataset, published in PDF format. This project<br> thesis was originally submitted on 18.04.2023 and supervised by Sebastian Pfaller. <br> <strong>Context</strong>: L. Laubert, "Establishing a framework for conducting comparative one- and<br> multidimensional studies on the coupling of the finite element method with<br> particle-based techniques", Project Thesis, Friedrich-Alexander-Universität<br> Erlangen-Nürnberg (FAU), 2023. <br> <strong>Abstract</strong>: This thesis presents a framework for conducting comparative one- and multidimensional<br> studies on the coupling of the finite element (FE) method with particle-based techniques.<br> The framework includes both a mathematical-mechanical description as well as<br> a code-based implementation for its execution: A one-dimensional (1D) setup imitates<br> the staggered scheme underlying coupled three-dimensional (3D) simulations, which are<br> based on the Capriccio method, and allows for a fast detection of parameter influences on<br> the system behavior. However, it lacks some features of typical 3D coupled systems, such<br> as nonlinear material behavior and particle interactions beyond the next neighbors. The<br> 1D model and its domains are set with equal dimensions corresponding to a reference<br> 3D system along the studied dimension. Significant quantities such as the number of<br> anchor points in the bridging domain and the stiffnesses of all domains are transformed<br> by various mathematical approaches for achieving interdimensional comparability. The<br> framework further includes a method for projecting mean displacements of molecular<br> dynamics (MD) particles, anchor points, and FE nodes of the 3D reference system along<br> the investigated spatial dimension to the corresponding coordinate axis of the 1D model.<br> This technique proves to be highly suitable for comparing the displacement behavior of<br> all domains of the 1D and 3D systems during deformation tests. To further demonstrate<br> the capabilities of the developed framework, the convergence behavior, measuring how<br> fast the coupled domains across the dimensions align, as well as the force responses in<br> the FE domain of the 1D model are compared to those of the 3D reference model. The<br> results show that the methods used for realizing interdimensional comparability result in<br> a rather similar convergence behavior as well as force responses of the 1D and 3D model.<br> Discrepancies observed between the 1D and 3D systems might be due to the limitations<br> of the 1D system imitating the 3D model, including the present inelastic behavior of the<br> 3D MD domain, and due to slight deliberately incorporated deviations in the domain<br> stiffnesses inside the coupling region of the 1D and 3D models. Overall, the present<br> work provides promising tools for conducting comparative studies on the coupling of<br> FEM with particle-based techniques, although further research is required to assess how<br> to eliminate or reduce the deviations. <br> <strong>Contact</strong>: Lukas Laubert<br> Institute of Applied Mechanics<br> Friedrich-Alexander-Universiät Erlangen-Nürnberg<br> Egerlandstraße 5<br> 91058 Erlangen <br> <strong>License</strong>: Creative Commons Attribution Non Commercial 4.0 International <br> <strong>Usage</strong>: All linked files can be downloaded. Individual instructions and installation guides are<br> provided in each dataset in seperate readme_*.txt files: 1D setup and execution scripts:<br> https://doi.org/10.5281/zenodo.7924400 3D to 1D projection scripts:<br> https://doi.org/10.5281/zenodo.7924406 3D reference models and deformation test results:<br> https://doi.org/10.5281/zenodo.7924441 <br> <strong>Citation</strong>: @thesis{laubert2023,<br> type = {Project thesis},<br> author = {Laubert, Lukas},<br> title = {Establishing a framework for conducting comparative one- and multidimensional studies on the coupling of the finite element method with particle-based techniques},<br> year = {2023},<br> school = {Friedrich-Alexander-Universit{\"a}t Erlangen-N{\"u}rnberg (FAU)}<br> }