Homogenization of a thermo-chemo-viscoelastic Kelvin-Voigt model

The paper is devoted to a model for the procedure of formation of a composite material constituted of solid fibers and of a solidifying matrix. The solidification process for the matrix depends on the temperature and on the degree of cure, which are used for the modeling of the mechanical properties of the matrix. Namely, the mechanical properties are described by Kelvin-Voigt viscoelastic equation with rapidly oscillating periodic coefficients depending on the temperature and the degree of cure. The latter are in turn solutions of a thermo-chemical problem with rapidly varying coefficients. We prove an error estimate for approximation of the viscoelastic problem by the same equation but with the coefficients depending on solution to the homogenized thermo-chemical problem. This estimate, in combination with our recent estimates for the viscoelastic (with time-dependent coefficients) and thermo-chemical homogenization problems, generates the overall error bound for the asymptotic solution to the full coupled thermo-chemo-viscoelastic model. (C) 2013 AIP Publishing LLC.