A lower semicontinuity result for some integral functionals in the space SBD

The purpose of this paper is to study the lower semicontinuity with respect to the strong L I convergence, of some integral functionals defined in the space SBD of special functions with bounded deformation. Precisely, we prove that, if U E SBD(Q), (u(h)) c SBD(Q) converges to u strongly in L 1 (Q, R-n) and the measures vertical bar E(j)u(h)vertical bar converge weakly * to a measure v singular with respect to the Lebesgue measure, then integral(Omega) f(x, Eu) dx <= lim inf h ->infinity integral(Omega) (x, Eu-h) dx provided the integrandf satisfies a weak convexity property and standard growth assumptions of order p > 1. (c) 2005 Elsevier Ltd. All rights reserved.