ASYMTOTIC HOMOGENIZATION OF COUPLED THERMO-VISCOELASTIC COMPOSITES WITH MULTIPLE SPATIAL AND TEMPORAL SCALES

摘要

A class of thermo-viscoelastic composites with microscopically periodic mechanical and thermal properties is studied using asymptotic homogenization method. A rapidly varying spatial scale and a fast temporal scale are introduced to capture the effects of spatial and temporal fluctuations induced by spatial heterogeneities and diverse time scales. The homogenized initial-boundary value problem along with the homogenized constitutive equations are derived up to the first order. It is shown that the homogenized solution retains the simplicity of the Kelvin-Voigt constitutive equation defined on the microscale and thus the computational efficiency is greatly enhanced compared to the classical spatial homogenization which gives rise to the long-term memory term in the homogenized constitutive equation. Numerical example reveals an excellent agreement between the proposed model and the reference solution obtained numerically with finite element mesh size on the scale of material heterogeneity.