A Mathematical Theory of the Mechanical Behavior of Continuous Media

Abstract

Until not long ago continuum mechanics meant to most people the theories of inviscid and linearly viscous fluids and of linearly elastic solids. However, the behavior of only few real materials can be described adequately by these classical theories. Experimental scientists, who had to deal with real materials, developed a science of non-classical materials called rheology. But they did not succeed in fitting their experimental results into a general mathematical framework. Most of the rheological theories are either one-dimensional, and hence appropriate at best for particular experimental situations, or are confined to infinitesimal deformations, in which case they are only of limited use, because large deformations occur easily in the materials these theories are intended to describe.