Constitutive branching in elastic materials

Abstract

AbstractIn finite elasticity a homogeneous strain is not always determined uniquely by the conjugate stress. The phenomenon is investigated for any constitutive work-function, and in both its global and local aspects. Uniqueness is lost in specific critical states. Basic properties of their aggregates in the stress and strain spaces are derived, and shown to be fundamental for the material response near individual critical states. The geometry of local branches is analyzed in detail. Further properties resulting from material isotropy are obtained. The general theory is illustrated by examples typifying the responses of metal crystals and rubberlike polymers.