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In this paper we investigate the equivalence of the sequentialweak lower semicontinuity of the total energy functional and the quasiconvexity of thestored 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 thatsatisfy the growth of order p≥ 1. This result is the mainstep towards the general existence theorem for the nonlinear micropolarelasticity.

In this paper we give an existence theorem for the equilibrium problem for nonlinear micropolar elastic body. We consider the problem in its minimization formulation and apply the direct methods of the calculus of variations. As the main step towards the existence theorem, under some conditions, we prove the equivalence of the sequential weak lower semicontinuity of the total energy and the quasiconvexity, in some variables, of the stored energy function.

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Semicontinuity theorem in the micropolar elasticity

Existence theorem for nonlinear micropolar elasticity

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2 results

Semicontinuity theorem in the micropolar elasticity

Existence theorem for nonlinear micropolar elasticity