Homogenization of Coupled Phenomena in Heterogenous Media

heterogeneous materials formed of various constituents with different properties and behaviours. Studies are usually carried out on volumes of materials that contain a large number of heterogeneities. Describing these media by using appropriate mathematical models to describe each constituent turns out to be an intractable problem. Instead they are generally investigated by using an equivalent macroscopic description - relative to the microscopic heterogeneity scale - which describes the overall behaviour of the media.

Fundamental questions then arise: Is such an equivalent macroscopic description possible? What is the domain of validity of this macroscopic description? The homogenization technique provides complete and rigorous answers to these questions.

This book aims to summarize the homogenization technique and its

contribution to engineering sciences. Researchers, graduate students and engineers will find here a unified and concise presentation.

The book is divided into four parts whose main topics are

- Introduction to the homogenization technique for periodic or

random media, with emphasis on the physics involved in the

mathematical process and the applications to real materials.

- Heat and mass transfers in porous media

- Newtonian fluid flow in rigid porous media under different

regimes

- Quasi-statics and dynamics of saturated deformable porous media

Each part is illustrated by numerical or analytical applications as

well as comparison with the self-consistent approach.