Simulation of shape memory cycle of a polymeric beam undergoing large deflection using a simple incremental approach

Abstract

Shape memory polymers are a group of polymers which can store a temporary shape at a relatively cold temperature and recover when heated above its glass transition temperature. Various constitutive models exist in literature to simulate the uniaxial shape memory cycle. One such popular model is based on the concept of multiple natural configurations. In the present work, the stress-strain-based model is adapted for bending application by converting it into a scalar moment-curvature-based relationship. The adapted model is used in a numerical framework for large deflection of beams to simulate the shape memory cycle. The employed numerical framework is based on linearising the non-linear governing differential equation and subsequently solving it in steps by numerical integration. The results are presented in suitable non-dimensional form for generality. Since coefficient of thermal expansion plays a minimal role in bending, it is found that the bending results are considerably different from their uniaxial counterpart. The approach may be claimed to be computationally economic as compared to finite element method because here large matrix inversion is avoided.