Thermomechanical modeling of a shape memory polymer

The aim of this work is to demonstrate a Helmholtz potential based approach for the development of the constitutive equations for a shape memory polymer undergoing a thermomechanical cycle. The approach is motivated by the use of a simple spring-dashpot type analogy and the resulting equations are classified as state-equations and suitable kinetic equations for the recoverable-energy elements and the dissipative elements in the model respectively. These elements have mechanical properties which vary with temperature. The governing equations of the model are developed starting from the basic conservation laws together with the laws of thermodynamics. The entire set of equations are written in a state-evolution form as a set of ordinary differential equations to be solved using Matlab. It is shown that the results of the simulation in Matlab are in qualitative and quantitative agreement with experiments performed on polyurethane. Subsequently, we study the dependence of the yield-stress on temperature to be similar and different functions of heating or cooling processes.