Modeling of polycrystalline shape memory alloys at finite strains based upon the logarithmic stress rate

Abstract
A thermomechanical model describing pseudoelasticity at finite strains is developed. It is Eulerian type and based upon the additive decomposition of the stretching D into an elastic and an elastic-inelastic phase transformation part and the multiplicative decomposition of the deformation gradient F into an elastic and an inelastic phase transformation part [1].

A thermodynamic framework with internal variables is utilized in order to explain the occurrence and evolution of the martensitic phase transformation [2]. The free energy for polycrystalline shape memory alloys is obtained from the specific free energies of the austenitic and martensitic phases and the interaction energy between them. The state of the material is determined by the temperature, the total strain and the total mass fraction of martensite. Suitable evolution laws for the latter and the transformation strain are proposed.