Variational asymptotic micromechanics of the effective time-dependent and pseudoelastic response of polymer matrix composites with shape memory alloy reinforcement

In order to effectively simulate the effective time-dependent and pseudoelastic response of shape memory alloy reinforced polymer matrix composites (SMA/PMCs), an incremental micromechanical model was constructed based on the variational asymptotic theory framework. Firstly, the incremental constitutive equations of polymer and shape memory alloys were derived, and a unified constitutive equation was established. Based on the unified constitutive equation, the variational expression of energy functional was derived. The incremental process associated with the instantaneous effective tangential matrix was constructed, solved and numerical implemented by the finite element method. The numerical examples show that the constructed model can be used to simulate the time-dependent pseudoelastic response of SMA/PMCs under different loading and temperature change rate, and accurately capture the rate-dependent and hysteretic behavior introduced by the viscoelastic behavior of polymer matrix.