Semicontinuity theorem in the micropolar elasticity

Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia. tambaca@math.hr; ivelcic@math.hr

Received: 24 July 2008

Abstract

In this paper we investigate the equivalence of the sequential weak lower semicontinuity of the total energy functional and the quasiconvexity of the stored energy function of the nonlinear micropolar elasticity. Based on techniques of Acerbi and Fusco [Arch. Rational Mech. Anal. 86 (1984) 125–145] we extend the result from Tambača and Velčić [ESAIM: COCV (2008) DOI: 10.1051/cocv:2008065] for energies that satisfy the growth of order p ≥ 1. This result is the main step towards the general existence theorem for the nonlinear micropolar elasticity.