Numerical homogenization techniques for the evaluation of mechanical behaviour of a composite with SMA inclusions

Numerical procedures are developed for the homogenization and evaluation of the stress field in a composite as a consequence of the presence of embedded SMA (shape-memory alloy) wires. In particular, the elastic field developed at the end of the SMA wire self-strain process is studied, knowledge of which is necessary to evaluate the feasibility of such a hybrid composite. First, the numerical procedures are applied to the study of both a representative volume element (RVE) included in a theoretically infinite periodic medium and a RVE located near the medium free boundary, in order to evaluate the tangential stress field generated at the end of the fiber; then they are applied to the study of a plate able to bend after the effect of self-strain of the SMA wire. Observations are reported about the obtained results and about the similarities and the differences between the two problems.