DYNAMIC THERMOELASTIC PROCESSES IN MICROPERIODIC COMPOSITES

Abstract

The aim of this article is to present (i) a formulation of the field equations characterizing a "refined averaged model" describing the dynamical thermoelastic processes in microperiodic composite materials, (ii) an analysis of particular models, and (iii) an application of an "effective modulus model" to solve a boundary initial value problem for a microperiodic layered semispace. Using a modeling procedure proposed in papers by Wo niak et al. [1,2], the fundamental field equations of coupled thermoelasticity for general microperiodic composite materials are derived and a one-dimensional layered composite model is obtained. The fundamental field equations involve the functions \\eqalign{{\\bf u}({\\bf x}, t) = {\\bf U} ({\\bf x}, t)+h^a({\\bf x}){\\bf V}^a({\\bf x}, t)\\cr \\vartheta({\\bf x}, t) =\\Theta({\\bf x}, t)+h^a({\\bf x})\\Phi^a({\\bf x}, t)\\qquad a=1,\\ldots ,n} where h a are the microshape functions; u and are the displacement and temperature fields, respectively; U , V a , , and | a are the basic unknown V-macrofunctions (V means a representative volume element). In a general case, a refined averaged model is described by a system of four partial differential equations for the displacement and temperature macrofunctions U and , coupled with a system of 4 n partial differential equations for the displacement and temperature microcorrectors V a and | a . In this case, the microstructure length-scale effect on the macrobehavior ofthecompositeistaken into account. In the framework of an effective modulus model the dynamical problem of thermal stresses for a composite semispace, corresponding to thermal shock on the surface x =0, has been formulated and solved in a closed form by a Laplace transform technique proposed by Ignaczak and the author [3]. The solutions obtained for the total temperature and stress fields are analyzed numerically and graphically. A survey of papers devoted to modeling layered thermoelastic composites including various homogenization theories is presented, among others, by Wo niak and Wierzbicki [2].