Curvature-dependent Eulerian interfaces in elastic solids
Analysis of PDEs
2024-02-16 v2
Abstract
We propose a sharp-interface model for a hyperelastic material consisting of two phases. In this model, phase interfaces are treated in the deformed configuration, resulting in a fully Eulerian interfacial energy. In order to penalize large curvature of the interface, we include a geometric term featuring a curvature varifold. Equilibrium solutions are proved to exist via minimization. We then utilize this model in an Eulerian topology optimization problem that incorporates a curvature penalization.
Cite
@article{arxiv.2305.02168,
title = {Curvature-dependent Eulerian interfaces in elastic solids},
author = {Katharina Brazda and Martin Kružík and Fabian Rupp and Ulisse Stefanelli},
journal= {arXiv preprint arXiv:2305.02168},
year = {2024}
}