Qualitative methods in continuum mechanics

Seepage theory deals with slow continuous flows in the multiply connected porespace of natural and man-made porous bodies such as soil, brick, or oil- and gas-bearing rocks. In contrast, fracture mechanics considers brittle or quasibrittle fracture of solids due to crack propagation. It is the generality of philosophy and mathematical methods that brings these two physically differing fields together and allows the treatment of both by common means and through a common approach. This Monograph gives a systematic presentation of basic approaches and techniques for using the integral functionals of solutions of some problems in continuum mechanics to derive estimates of local and integral quantities of interest, thus avoiding the necessity for a detailed solution of the problems. Problems in the theory of fluid flow through porous media, elasticity, and fracture mechanics are considered in some detail, and results derived from the use of these methods are also presented. The book will be of interest to researchers and teachers in continuum mechanics, applied mathematics, mechanical engineering, and hydrology. It will also be useful for undergraduate and postgraduate students in these fields.