A simple, Gibbs potential based multinetwork model for shape memory polymers

The aim of this paper is to demonstrate a Gibbs potential based approach for the development of the constitutive equations for a shape memory polymer where the shape retention and recovery upon heating is controlled by a glass transition process. The approach is motivated by the use of a simple spring-dashpot type analogy and the resulting equations are classified as state equations for the thermoelastic spring like response and a kinetic equation for the frictional dashpot. The governing equations are written in a state evolution form as a set of ordinary differential equations to be solved. The entire set of equations are developed starting from the basic conservation laws for a wire together with the laws of thermodynamics. The solution for a simple thermomechanical shape setting and recovery cycle is obtained using Matlab. It is shown that the results are in qualitative agreement with experiments performed on polyurethane.