On Thermodynamic Consistency of a Stochastic Constitutive Model for Glassy Polymers

Abstract

A full understanding of the thermomechanical behavior of materials in the glassy state remains one of the outstanding challenges in condensed matter physics. A recently developed stochastic constitutive model (SCM) that explicitly acknowledges nanoscale dynamic heterogeneity has had success in describing a number of nonlinear mechanical and relaxation experiments. The model employs stochastic differential equations to describe evolution of the local thermodynamic variables of entropy and the stress tensor, where the magnitude of the fluctuations is itself a strong nonlinear function of these variables. Notwithstanding the successes of the model, there is a legitimate question whether the formulation is thermodynamically consistent because, unlike the SCM, the stochastic systems treated in the literature satisfy the fluctuation dissipation theorem and assume constant magnitude of fluctuations. We propose expression for the free energy that results in fulfilment of the H-theorem statement and develop the second law in the Clausius–Duhem form for the SCM, where the expression for the power of the external driving forces is modified in the stochastic case as compared to that in standard continuum mechanics.