Homogenization techniques for the analysis of porous SMA

In this paper the mechanical response of porous Shape Memory Alloy (SMA) is modeled. The porous SMA is considered as a composite medium made of a dense SMA matrix with voids treated as inclusions. The overall response of this very special composite is deduced performing a micromechanical and homogenization analysis. In particular, the incremental Mori-Tanaka averaging scheme is provided; then, the Transformation Field Analysis procedure in its uniform and nonuniform approaches, UTFA and NUTFA respectively, are presented. In particular, the extension of the NUTFA technique proposed by Sepe et al. (Int J Solids Struct 50:725-742, 2013) is presented to investigate the response of porous SMA characterized by closed and open porosity. A detailed comparison between the outcomes provided by the Mori-Tanaka, the UTFA and the proposed NUTFA procedures for porous SMA is presented, through numerical examples for two- and three-dimensional problems. In particular, several values of porosity and different loading conditions, inducing pseudoelastic effect in the SMA matrix, are investigated. The predictions assessed by the Mori-Tanaka, the UTFA and the NUTFA techniques are compared with the results obtained by nonlinear finite element analyses. A comparison with experimental data available in literature is also presented.