On the Micromodelling of Dynamic Response for Thermoelastic Periodic Composites

Abstract

As it is known, the asymptotic homogenization methods for micro-periodic composites, leading to the effective modulus theories, neglect inertial aspects of microstructural features related to the size of constituents (cf. [1,2] and the references therein). The main aim of this contribution is to propose a new approach to the formulation of macro-models for micro-periodic thermoelastic composite materials. This approach takes into account a length-scale effect on a dynamic response of a composite and is simple enough to be applied in analysis of engineering problems and for quasi-stationary processes reduces to the special effective modulus theory, [3,4]. Theories of this type for elastic composite materials and structures were discussed in [5–7] and are termed refined macro-theories. In this paper governing equations of the refined macro--thermoelastodynamics are formulated on the basis of heuristic hypotheses concerning the expected form of disturbances in displacement and temperature fields, caused by the micro-inhomogeneity of a composite. At the same time a special form of macro-modelling approximations is used. The resulting equations are obtained without any reference to a boundary value problem on the representative volume element, that is required in asymptotic homogenization approaches, [1,2]. The general considerations are illustrated by the simple example the aim of which is to compare results of the refined macro-theory and those of the effective modulus theory. It is shown that the microstructure length scale effects, described by the proposed macro-theory, play an essential role in investigations of the non-stationary behaviour of the composites.