Functionals defined on piecewise rigid functions: Integral representation and $\Gamma$-convergence
Abstract
We analyze integral representation and -convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component is constant and lies in a set without rank-one connections. Such functionals account for interfacial energies in the variational modeling of materials which locally show a rigid behavior. Our results are based on localization techniques for -convergence and a careful adaption of the global method for relaxation (Bouchitt\'e et al. 1998, 2001) to this new setting, under rather general assumptions. They constitute a first step towards the investigation of lower semicontinuity, relaxation, and homogenization for free-discontinuity problems in spaces of (generalized) functions of bounded deformation.
Cite
@article{arxiv.1904.06305,
title = {Functionals defined on piecewise rigid functions: Integral representation and $\Gamma$-convergence},
author = {Manuel Friedrich and Francesco Solombrino},
journal= {arXiv preprint arXiv:1904.06305},
year = {2020}
}