Crack occurrence in bodies with gradient polyconvex energies
Analysis of PDEs
2022-01-19 v1
Abstract
Energy minimality selects among possible configurations of a continuous body with and without cracks those compatible with assigned boundary conditions of Dirichlet-type. Crack paths are described in terms of curvature varifolds so that we consider both \textquotedblleft phase" (cracked or non-cracked) and crack orientation. The energy considered is gradient polyconvex: it accounts for relative variations of second-neighbor surfaces and pressure-confinement effects. We prove the existence of minimizers for such an energy. They are pairs of deformations and varifolds. The former ones are taken to be maps satisfying an impenetrability condition. Their jump set is constrained to be in the varifold support.
Keywords
Cite
@article{arxiv.2102.06641,
title = {Crack occurrence in bodies with gradient polyconvex energies},
author = {Martin Kružík and Paolo Maria Mariano and Domenico Mucci},
journal= {arXiv preprint arXiv:2102.06641},
year = {2022}
}