Micromechanics and Homogenization of SMA-Wire-Reinforced Materials

Abstract

The aim of the paper is to develop a micromechanical model for the evaluation of the overall constitutive behavior of a composite material obtained embedding SMA wires into an elastic matrix. A simplified thermomechanical model for the SMA inclusion, able to reproduce the superelastic as well as the shape memory effect, is proposed. It is based on two assumptions: the martensite volume fraction depends on the wire temperature and on only the normal stress acting in the fiber direction; the inelastic strain due to the phase transformations occurs along the fiber direction. The two introduced hypotheses can be justified by the fact that the normal stress in the fiber direction represents the main stress in the composite. The overall nonlinear behavior of long-fiber SMA composites is determined developing two homogenization procedures: one is based on the Eshelby dilute distribution theory, the other considers the periodicity conditions. Numerical applications are developed in order to study the thermomechanical behavior of the composite, influenced by the superelastic and shape memory effects occurring in the SMA wires. Comparisons of the results obtained adopting the two homogenization procedures are reported. The influence of the matrix stiffness and of a prestrain in the SMA wires on the overall behavior of the composites is investigated.