Nonlinear thermoelasticity of ferroelastics (Q1269798)

A ferroelastic crystal is defined as a crystal which has at least two orientation states that differ in at least one of the components of the spontaneous strain tensor. A suitably oriented uniaxial stress can switch one ferroelastic state to another, and strain-stress hysteresis is a salient feature of ferroelastic materials. In this work, the authors propose a constitutive theory by choosing a set of independent constitutive variables which consist of the Cauchy stress tensor, temperature, temperature gradient, heat flux vector and a set of internal variables called anisotropy-grain tensors. For the heat flux vector and internal variables, appropriate evolution equations are derived. Then the standard use of the well-known entropy inequality yields the desired constitutive relations in terms of Helmholtz free energy and a vector thermodynamical potential. The authors also give isotropic constitutive relations for strain tensor and for the evolution of heat flux vector. There are no applications which prove that the proposed constitutive relations describe satisfactorily the expected behaviour of ferroelastic materials.