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

Abstract

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.

References in corpus (5)

• A density result in $GSB{D}^p$ with applications to the approximation of brittle fracture energies
• Integral representation for functionals defined on $SB{D}^p$ in dimension two
• Density of polyhedral partitions
• Functionals defined on piecewise rigid functions: Integral representation and $\Gamma$-convergence
• On the approximation of $SBD$ functions and some applications