Numerical simulation of shape memory alloys structures using interior-point methods

This paper is concerned with the numerical simulation of quasi-static evolutions in shape memory alloys structures. In micromechanical models of shape memory alloys, the phase transformation is described by an internal variable representing the volume fractions of the different variants of martensite. In contrast with the framework of standard plasticity, that internal variable is physically constrained to satisfy a set of inequalities at each point. From a structural simulation point of view, handling such local constraints in the evolution problem is not obvious. Robustness and computational time are particularly sensitive issues. In this paper is proposed a new approach which essentially consists in reformulating the non-linear incremental problem as a linear complementarity problem. That approach notably calls for an easy implementation in FEM codes. Comparison with some experimental and numerical results from literature shows the relevancy of the proposed approach.