This book is devoted to describing theories for porous media where such
pores have an inbuilt macro structure and a micro structure. For
example, a double porosity material has pores on a macro scale, but
additionally there are cracks or fissures in the solid skeleton. The
actual body is allowed to deform and thus the underlying theory is one
of elasticity. Various different descriptions are reviewed.
Chapter 1 introduces the classical linear theory of elastodynamics
together with uniqueness and continuous dependence results. Chapters 2
and 3 review developments of theories for double and triple porosity
using a pressure-displacement structure and also using
voids-displacement. Chapter 4 compares various aspects of the
pressure-displacement and voids-displacement theories via uniqueness
studies and wave motion analysis. Mathematical analyses of double and
triple porosity materials are included concentrating on uniqueness and
stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis
is on wave motion in double porosity materials with special attention
paid to nonlinear waves. The final chapter embraces a novel area where
an elastic body with a double porosity structure is analyzed, but the
thermodynamics allows for heat to travel as a wave rather than simply by
diffusion.
This book will be of value to mathematicians, theoretical engineers and
other practitioners who are interested in double or triple porosity
elasticity and its relevance to many diverse applications.
