On the simultaneous solution of structural membranes on all level sets within a bulk domain

DOI10.1016/J.CMA.2023.116223arXiv2305.20001OpenAlexW4385011215MaRDI QIDQ6096465

Thomas-Peter Fries, Michael Wolfgang Kaiser

Publication date: 12 September 2023

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Abstract: A mechanical model and numerical method for structural membranes implied by all isosurfaces of a level-set function in a three-dimensional bulk domain are proposed. The mechanical model covers large displacements in the context of the finite strain theory and is formulated based on the tangential differential calculus. Alongside curved two-dimensional membranes embedded in three dimensions, also the simpler case of curved ropes (cables) in two-dimensional bulk domains is covered. The implicit geometries (shapes) are implied by the level sets and the boundaries of the structures are given by the intersection of the level sets with the boundary of the bulk domain. For the numerical analysis, the bulk domain is discretized using a background mesh composed by (higher-order) elements with the dimensionality of the embedding space. The elements are by no means aligned to the level sets, i.e., the geometries of the structures, which resembles a fictitious domain method, most importantly the Trace FEM. The proposed numerical method is a hybrid of the classical FEM and fictitious domain methods which may be labeled as "Bulk Trace FEM". Numerical studies confirm higher-order convergence rates and the potential for new material models with continuously embedded sub-structures in bulk domains.

Full work available at URL: https://arxiv.org/abs/2305.20001

zbMATH Keywords

fictitious domain method level-set method finite strain theory trace FEM embedded domain method ropes and membranes

Mathematics Subject Classification ID

Mechanics of deformable solids (74-XX) Quantum theory (81-XX)

Cites Work