3D hierarchical multiscale analysis of heterogeneous SMA based materials

A 3D hierarchical multiscale computational homogenization framework with periodic Representative Volume Element (RVE) is proposed in the present study for analysis of shape memory alloy (SMA) fiber reinforced composite and porous SMA specimen. The shape memory alloy, which exhibits forward and reverse transformations, is wired through a matrix, while a dense SMA matrix encircles voids as inclusions in the porous model. The asymptotic mathematical homogenization approach is used to express the microscopic and macroscopic governing equations. An iterative solution is used at each point in order to derive the tangential constitutive response of the corresponding periodic RVE. Several numerical problems are solved and the results are compared with those obtained from a fully meshed direct numerical model. Detailed discussions are presented regarding the distribution of field variables, in particular the martensitic volume fraction and the stress state inside RVEs located at critical points of the macro models, subjected to cyclic stress loads in the form of tension, flexure and torsion. Moreover, a micromechanical analysis is conducted to investigate the effect of the shape of ellipsoid porosities on the overall response of porous SMA.