A three-dimensional phenomenological constitutive model for porous shape memory alloys including plasticity effects

Porous shape memory alloys are a class of very interesting materials exhibiting features typical of porous metals and of shape memory alloys. In contrast to dense shape memory alloys, considerable plastic strain accumulates in porous shape memory alloys even during phase transformation. Moreover, due to the microstructure of porous materials, phase transformation and plasticity phenomena are significantly pressure-dependent. In this article, we propose a three-dimensional phenomenological constitutive model for the thermomechanical behavior of porous shape memory alloys able to predict shape memory effect, pseudo-elastic behavior and plastic behavior under proportional as well as non-proportional multiaxial loadings. To this end, proper internal variables together with free energy and limit functions are introduced. The material parameters are determined for several available porous shape memory alloys with a wide range of porosity (from 16% to 51%), and a good agreement between numerical predictions of the proposed model and experimental results is observed. Moreover, plastic and transformation strain evolution during increasing and decreasing cyclic loadings are demonstrated through several examples. Finally, to show model capabilities, shape memory effect and pressure-dependent behavior as well as model response under non-proportional loadings are also presented.