An Introduction to Non-Linear Continuum Mechanics

Abstract

Since the Second World War there has been a considerable interest in the development of phenomenological theories describing the relation between force and deformation in bodies of material which do not obey either the linear laws of the classical theories of elasticity and the hydrodynamics of viscous fluids, or the simple and explicit non-linear laws of gas dynamics.Since the Second World War there has been a considerable interest in the development of phenomenological theories describing the relation between force and deformation in bodies of material which do not obey either the linear laws of the classical theories of elasticity and the hydrodynamics of viscous fluids, or the simple and explicit non-linear laws of gas dynamics.

During the first half of the present century much effort has been devoted to the elaboration of these classical theories and their application to specific problems of importance in - or at any rate suggested by - some area of science and technology. During this period the development of nonlinear theories in the same rational spirit as inspired the development of the classical theories in the nineteenth century was, in large measure, neglected. This was undoubtedly due, at any rate in part, to a preoccupation with the more developed theories which were nearer the point at which they might provide some insight into technological or scientific problems.