Computational micro to macro transitions for shape memory alloy composites using periodic homogenization

Abstract

In the current manuscript, a homogenization framework is proposed for periodic composites with shape memory alloy (SMA) constituents under quasi-static thermomechanical conditions. The methodology is based on the step-by-step periodic homogenization, in which the macroscopic and the microscopic problems of the composite are solved simultaneously. The implementation of the framework is examined with numerical examples on SMA composite laminates. Complexity of the composite nonlinear response and non-proportional stress state in the SMA appears, even in the case of uniaxial macroscopic boundary conditions. Moreover, under certain conditions, the composite laminate can exhibit a non-convex transformation surface. Additionally, the transformation temperatures at various stress levels under isobaric thermal cycling can be quite different between the composite and the pure SMA.