A Two-network thermomechanical model 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 model is able to simulate the response of the material during heating and cooling cycles and the sensitive dependence of the response on thermal expansion. We notice that the yield-stress of the material controls the gross features of the response of the model, and suggests that the material yields differently depending on not just the current value of the temperature but also on whether the temperature of the material dropped or increased from the previous time-step somewhat similar to the Bauschinger effect in plasticity, except that here the controlling parameter is the rate of temperature change rather than rate of plastic strain. The results of the simulation are in qualitative and quantitative agreement with experiments performed on two different shape memory polymer samples: polyurethane and epoxy resin. We find that modeling the hysteresis of the yield stress of the material during temperature changes is the key to the results.