METHOD OF ASYMPTOTIC HOMOGENIZATION OF THERMOVISCOELASTICITY EQUATIONS IN PARAMETRIC SPACE: PART I (THEORETICAL)
Alex N. Vlasov, D. B. Volkov‐Bogorodsky · Composites Mechanics Computations Applications An International Journal · 2018
In the paper, a two-level scheme is substantiated for representing solutions for thermoviscoelasticity equations with fast oscillating coefficients corresponding to a structurally inhomogeneous viscoelastic medium with nonlinear characteristics. In contrast to the traditional approach based on the classical method of asymptotic homogenization, here, in the analysis of the thermoviscoelasticity equations, additional nonlinear dependences of the material characteristics on temperature and on spatial coordinates are taken into account. To this end, the asymptotic homogenization procedure is formulated in such a way that the nonlinear dependences, which have a smoothly changing character against a background of fast oscillations of the coefficients, are resolved parametrically in the asymptotic analysis of the equations. As a result, a two-level scheme for representing solutions of thermoviscoelastic problems is formulated, which makes it possible to determine the effective rheological characteristics of a structurally inhomogeneous material and to obtain a stress relaxation pattern taking into account the internal microstructure.