Three-dimensional model of thermomechanical evolution of shape memory materials

We derive a thermodynamically consistent model of the thermomechanical evolution of shape memory materials in three dimensions. The model is based on the linearized strain tensor and the absolute temperature as state variables. It accounts for the viscous and spatially nonlocal effects, and constitutes a generalization of the one-dimensional Falk model. The constitutive equations comply with the entropy inequality. Examples of free energies characteristic for shape memory alloys and noncrystalline materials are given.