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Semicontinuity theorem in the micropolar elasticity

Josip Tambača;  Igor Velčić — 2010

ESAIM: Control, Optimisation and Calculus of Variations

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 [ (1984) 125–145] we extend the result from Tambača and Velčić [ (2008) DOI: 10.1051/cocv:2008065] for energies that satisfy the growth of order 1. This result is the main step towards the general existence theorem...

Existence theorem for nonlinear micropolar elasticity

Josip Tambača;  Igor Velčić — 2010

ESAIM: Control, Optimisation and Calculus of Variations

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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