A thermodynamically-consistent 3 D constitutive model for shape memory polymers

The ever increasing applications of shape memory polymers have motivated the development of appropriate constitutive models for these materials. In this work, we present a 3 D constitutive model for shape memory polymers under time-dependent multiaxial thermomechanical loadings in the small strain regime. The derivation is based on an additive decomposition of the strain into six parts and satisfying the second law of thermodynamics in Clausius–Duhem inequality form. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. The viscous effects are also fully accounted for in the proposed model. Further, we present the time-discrete form of the evolution equations in the implicit form. The model is validated by comparing the predicted results with different experimental data reported in the literature. Finally, using the finite element method, we solve two boundary value problems e.g., a 3 D beam and a medical stent made of shape memory polymers.

► Proposing evolution laws during not only cooling but also heating process. ► Considering viscous effects by employing separate parallel elements in each phase. ► Presenting the numerical implementation of the 3 D constitutive model. ► Predicting the behavior of SMP foams by considering a hard segment in the model. ► The model is thermodynamically consistent.