Equations of thermomechanics of deformable bodies with regard for irreversibility of local displacement of mass

Abstract

Using the basic principles of thermodynamics of nonequilibrium processes and continuum mechanics, we obtain a complete set of equations for the description of coupled thermomechanical processes in a deformable solid with regard for irreversibility of the process of local displacement of mass. The space gradient $ \boldsymbol{\nabla}_{\mu_{\pi}^{\prime}} $ of the reduced energy measure of the influence of the displacement of mass on the internal energy is represented in the form of the sum of the reversible and irreversible components. This enables us to obtain an integral relation of the convolution type with exponential kernel of relaxation for determination of the vector of displacement of mass π m . Moreover, the vector π m is defined not only by the history of $ \boldsymbol{\nabla}_{\mu_{\pi}^{\prime}} $ but also by the history of the temperature gradient ∇ T . The key equations of the proposed model are written in the linearized approximation and the corresponding boundary conditions are formulated.