Effective thermodynamic potentials and internal variables: Particulate thermoviscoelastic composites

Abstract

The problem addressed in this study is the full coupling between three different contributions to the strain in thermoviscoelastic composites, elasticity, viscosity and temperature changes. It shows that even in simple situations, the coupling with temperature may lead to counter-intuitive effects which are not accounted for through the sole overall stress–strain relations. The correspondence principle permits to express the macroscopic strain–stress relation and the macroscopic entropy as a set of ordinary differential equations for two types of effective internal variables, mechanical variables on the one hand and thermal variables on the other hand. Interpreting the macroscopic response as a rheological generalized Maxwell model allows us to compute the macroscopic free energy and the dissipated energy of the composite in terms of these internal variables. Coupled with Hashin–Shtrikman estimates, these thermodynamic functions provide additional information on the statistics of the stress field when the composite is subjected to a mixed loading combining mechanical and thermal effects.