Calculus of Variations and Geometric Measure Theory

M. Cicalese - M. Focardi - C. I. Zeppieri

Phase-field approximation of functionals defined on piecewise-rigid maps

created by zeppieri1 on 01 Apr 2021
modified by cicalese on 25 Jun 2022


Published Paper

Inserted: 1 apr 2021
Last Updated: 25 jun 2022

Journal: J. Nonlinear Sci.
Volume: 31
Number: 5
Pages: Paper No. 78, 25pp
Year: 2021


We provide a variational approximation of Ambrosio-Tortorelli type for brittle fracture-energies of piecewise-rigid solids. Our result covers both the case of geometrically nonlinear elasticity and that of linearised elasticity.

Keywords: Brittle fracture, $\Gamma$-convergence, Free-discontinuity problems, Phase-field models, Geometric rigidity, elliptic approximation, piecewise-rigid maps, linearised elasticity