An implicit thermomechanical theory based on a Gibbs potential formulation for describing the response of thermoviscoelastic solids
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The aim of this paper is to develop an implicit constitutive for the thermoviscoelastic behavior of polymers, based on a thermomechanical framework. The core idea is to assume that the response of the material can be modeled as that of multiple superposed networks whose stresses are additive. The thermomechanical response is then developed based on the Gibbs potential of the networks (which is assumed to be a function of the individual network stresses and the temperature) and a rate of dissipation function. The approach results in a set of implicit rate equations for the stresses (without the need for explicitly postulating viscoelastic or inelastic strain as a primitive variable) that is easily amenable to analysis. We demonstrate how certain "internal clock" models as well as anisotropic integral type models can be derived within the context of such an approach. We compare the predictions of the model with the published experimental results concerning the thermoviscoelastic response of FM 13 Adhesive and demonstrate both the simplicity of the approach as well as the efficacy of the model in predicting the complex behavior of such adhesives. 2013 Published by Elsevier Ltd.
