Abstract

In this paper we study the equilibrium deformations of an incompressible elastic body with a non-convex strain energy function which is subjected to a homogeneous distribution of dead-load tractions. To determine the stable solutions we consider the mixtures of the phases which minimize the total energy density. In the special case of a trilinear material we discuss the stability of the equilibrium phases in detail. Finally, we show that multiphase solutions are possible when the surface loads correspond to a critical simple shear and we sketch their possible forms.

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