The quasi-homogenized Bakhvalov–Eglit model of a thermoviscoelastic material beyond the periodic setting

The one-dimensional model of dynamics of a thermoviscoelastic Kelvin–Voigt material provided with rapidly oscillating initial distributions of specific volume, velocity, and specific internal energy is considered. It is allowed that the rapidly oscillating initial distributions do not have any ordered microstructure: periodic, quasi-periodic, random homogeneous, and so on. We rigorously justify the homogenization procedure as the frequency of rapid oscillations tends to infinity. As the result, we construct a closed limit effective model of a thermoviscoelastic material motion. This model contains an additional kinetic equation that carries complete information on the evolution of the limit oscillation regimes. We show that if the initial data are periodic, then the constructed limit model can be reduced to a system of the classical quasi-homogenized Bakhvalov–Eglit equations.