Calculus of Variations and Geometric Measure Theory
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M. Kruzik - P. M. Mariano - D. Mucci

Crack occurrence in bodies with gradient polyconvex energies

created by mucci on 18 Feb 2021

[BibTeX]

Submitted Paper

Inserted: 18 feb 2021
Last Updated: 18 feb 2021

Pages: 22
Year: 2021
Links: Link to Arxiv

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 "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 existence of minimizers for such an energy. They are pairs of deformations and varifolds. The former ones are taken to be $SBV$ maps satisfying an impenetrability condition. Their jump set is constrained to be in the varifold support.

Keywords: calculus of variations, microstructures, varifolds, shells, fracture, ground states


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