Integral representation for energies in linear elasticity with surface discontinuities

摘要: In this paper we prove an integral representation formula for a general class of energies defined on the space generalized special functions bounded deformation ($GSBD^p$) in arbitrary dimensions. Functionals type naturally arise modeling linear elastic solids with surface discontinuities including phenomena as fracture, damage, tension between different phases, or material voids. Our approach is based global method relaxation devised Bouchitte et al. '98 and recent Korn-type inequality $GSBD^p$ (Cagnetti-Chambolle-Scardia '20). strategy also allows to generalize results $SBD^p$, obtained dimension two (Conti-Focardi-Iurlano '16), higher dimensions, revisit framework variation ($GSBV^p$).