A thermomechanical constitutive model for porous SMAs accounting for the influence of void evolution

Abstract

A new thermomechanical constitutive model is proposed for shape memory alloys (SMAs) with randomly distributed microscopic porosity. The influence of the microscopic voids on SMA behavior is accounted for by means of two scalar variables representing damage due to porosity and inelastic dilatation due to the expansion or shrinking of voids. Starting with a newly formulated expression of the Helmholtz free energy density, a general stress-strain relation is derived for porous SMAs. The relation features internal dissipative variables for which thermodynamically consistent flow rules are proposed. In particular, loading functions are obtained for variables representing the volume fraction of martensite, inelastic strain due to martensite detwinning and reorientation, as well as damage and inelastic dilatation caused by the presence and evolution of voids. Appropriate loading conditions and flow rules are then introduced in a way that satisfies the principles of thermodynamics. The model is numerically integrated using a multi-surface return mapping algorithm implemented in a finite element software. The integration procedure, including the formulation of the required time-discrete equations and the derivation of the material Jacobian are presented in detail. The developed model is validated by two sets of experimental results and one modeling work to good agreement. The model is then used for simulating reference stress-strain data taken from the literature, in addition to test cases showcasing the ability of the model to simulate complex structures in presence of non-proportional loading and strong stress gradients.