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Composites: Mechanics, Computations, Applications: An International Journal
ESCI SJR: 1.182 SNIP: 0.125 CiteScore™: 0.23

ISSN Print: 2152-2057
ISSN Online: 2152-2073

Composites: Mechanics, Computations, Applications: An International Journal

DOI: 10.1615/CompMechComputApplIntJ.2018026528
pages 331-343

METHOD OF ASYMPTOTIC HOMOGENIZATION OF THERMOVISCOELASTICITY EQUATIONS IN PARAMETRIC SPACE: PART I (THEORETICAL)

A. N. Vlasov
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky Ave., Moscow, 125040, Russian Federation
Dmitriy B. Volkov-Bogorodsky
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky Ave., Moscow, 125040, Russia

ABSTRACT

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.