Thermodynamic and statistical principles of the theory of elastoviscoplastic deformation and strengthening of materials

We propose a thermodynamic method and a statistical one for constructing the constitutive equations of elastoviscoplastic deformation and strengthening of materials. The thermodynamic method is based on the energy conservation law as well as the equations of entropy balance and entropy generation in the presence of self-equilibrated internal microstresses, which are characterized by coupled strengthening parameters. The general constitutive equations consist of the relations between thermodynamic flows and forces, which follow from nonnegativity of entropy generation and satisfy the generalized Onsager principle, as well as the thermoelasticity relations and the expression for entropy, which follow from the energy conservation law. The specific constitutive equations are obtained on the basis of representation of the energy dissipation rate as a sum of two constituents that describe translational and isotropic strengthening and are approximated by power and hyperbolic sine laws. Starting from the stochastic microstructural concepts, we construct the constitutive equations of elastoviscoplastic deformation and strengthening on the basis of the linear model of thermoelasticity and the nonlinear Maxwell model for spherical and deviatoric components of microstresses and microstrains, respectively. The solution of the problem of the effective properties and stress-strain state of a three-component material is constructed with the use of the combined Voigt–Reuss scheme and leads to constitutive equations coinciding, as to their form, with similar equations constructed by the thermodynamic method.