A phenomenological model for shape memory alloys with uniformly distributed porosity

A phenomenological model is proposed for shape memory alloys considering the presence of uniformly distributed voids. The model is developed within a modified generalized standard materials framework, which considers the presence of constraints on the state variables and ensures thermodynamic consistency. Within this framework, a free energy density is first proposed for the porous material, wherein the influence of porosity is accounted for by means of scalar state variables accounting for damage and inelastic dilatation. By choosing key thermodynamic forces, derived from the expression of the energy, as sub-gradients of a pseud-potential of dissipation, loading functions are derived that govern phase transformation and martensite detwinning. Flow rules are also proposed for damage and inelastic dilatation in a way that ensures positive dissipation. The model is discretized and the integration of the time-discrete formulation is carried out using an implicit formulation, whereby a return mapping algorithm is implemented to calculate increments of dissipative variables including inelastic strains. Comparison with data from the literature is finally presented.