A two-network thermomechanical model and parametric study of the response of shape memory polymers
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In this work, we develop a three-dimensional continuum two-network model for the thermoelastic response of a shape memory polymer and study the influence of the material parameters on the response characteristics of the model. Rather than an integral type viscoelastic model, the approach here is based on the idea of two inter-penetrating networks, one which is permanent and the other which is transient together with rate equations for the time evolution of the transient network. We find that the activation stress for network breakage and formation of the material controls the gross features of the response of the model, and exhibits a "thermal Bauschinger effect". A systematic parameter optimization method with different weights given to different features of the response is used to match the material parameters with experimental data. A parametric study is carried out, that varies each of the model material parameters, and observes their effect on design-relevant response characteristics of the model undergoing a thermomechanical cycle. We develop "response charts" for the response characteristics: shape fixity, shape recovery and maximum stress rise during cooling, to give the designer an idea of how the simultaneous variation of two of the most influential material parameters changes a specific response parameter. This study shows that based on this model, among all the material parameters i.e. the glassy and rubbery modulus, thermal expansion and viscosity, as well as the coefficients of the heating and cooling activation stress function, the primary variables that have considerable effect on the response of the material are the rubbery modulus and certain coefficients of the hysteretic activation stress functions. Finally we show validation results for two different shape memory phenomena: unconstrained shape recovery and constrained stress recovery. 2013 Elsevier Ltd. All rights reserved.
