Functionals defined on piecewise rigid functions: Integral representation and $\Gamma$-convergence

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