We analyse integral representation and Γ-convergence properties of functionals defined on piecewise rigid functions, that is, 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 Γ-convergence and a careful adaption of the global method for relaxation (Bouchitté et al. in Arch Ration Mech Anal 165:187–242, 2002; Bouchitté et al. in Arch Ration Mech Anal 145:51–98, 1998), 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.
Functionals Defined on Piecewise Rigid Functions: Integral Representation and Γ -Convergence / Friedrich, M.; Solombrino, F.. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 236:(2020), pp. 1325-1387. [10.1007/s00205-020-01493-8]
Functionals Defined on Piecewise Rigid Functions: Integral Representation and Γ -Convergence
Friedrich M.;Solombrino F.
2020
Abstract
We analyse integral representation and Γ-convergence properties of functionals defined on piecewise rigid functions, that is, 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 Γ-convergence and a careful adaption of the global method for relaxation (Bouchitté et al. in Arch Ration Mech Anal 165:187–242, 2002; Bouchitté et al. in Arch Ration Mech Anal 145:51–98, 1998), 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.