Application of Thermodynamics to Thermomechanical, Fracture, and Birefringent Phenomena in Viscoelastic Media

Abstract

A unified theory of the thermomechanical behavior of viscoelastic media is developed from studying the thermodynamics of irreversible processes, and includes discussions of the general equations of motion,crack propagation, and birefringence. The equations of motion in terms of generalized coordinates and forces are derived for systems in the neighborhood of a stable equilibrium state. They represent a modification of Biot's theory in that they contain explicit temperature dependence, and a thermodynamically consistent inclusion of the time‐temperature superposition principle for treating media with temperature‐dependent viscosity coefficients. The stress‐strain‐temperature and energy equations for small deformation behavior follow immediately from the general equations and, along with equilibrium and strain‐displacement relations, they form a complete set for the description of the thermomechanical behavior of media with temperature‐dependent viscosity. The role of thermodynamics in finite deformation and crack propagation problems is examined. Restrictions placed on the constitutive equations by thermodynamics is illustrated by considering a familiar stress‐strain equation for polymers, wherein the time and strain dependence of stress in a relaxation test appear as separate factors. In addition, an energy equation for crack propagation is derived and then applied to a specific problem. Thermodynamic implications concerning birefringence are also discussed and an operational stress‐optical coefficient is derived.