Qualitatively new models of microinhomogeneous media obtained by homogenization

Abstract

Averaged effective models for inhomogeneous media with constituents of very different properties, in particular, composites, mixtures, and porous materials are considered in this paper. It is known that effective properties of composites and mixtures may differ from their components properties not only quantitatively but also qualitatively. The paper aims to demonstrate examples of appearance of qualitatively new models as a result of homogenization procedure. Media consisting of qualitatively similar components are considered. The following effective models are described: models with higher derivatives that describe dispersion of waves in composites consisting of elastic components while there is no dispersion of waves in individual components; models of compressive media for incompressible elastic materials with pores; models with long-range memory or with additional internal parameters for mixtures of viscous fluids as well as for composites consisting of elastoplastic components; models for sound propagation in mixtures of fluids that are different depending on relations between the inhomogeneity length scale and parameters linked with fluids viscosity and heat conductivity.The paper is a brief review of the results obtained by N.S. Bakhvalov and the author.