Introduction

Summary

The purpose of the present book is to give an idea about fundamental concepts and methods, as well as instructive special results, of a unified intermediate asymptotic mathematical theory of the flow, deformation and fracture of real fluids and deformable solids. This theory is based on a quite definite and, we emphasize, idealized approach where the real materials are replaced by a continuous medium; therefore it is often called the mechanics of continua. It generalizes, and represents from a unified viewpoint, more focused disciplines: fluid dynamics, gas dynamics, the theory of elasticity, the theory of plasticity etc. For various reasons these disciplines underwent separate development for a long time. The splendid exceptions found in the work of A. L. Cauchy, C. L. M. H. Navier and A. Barré de Saint-Venant in the nineteenth century and L. Prandtl, Th. von Kármán, and G. I. Taylor in the twentieth century confirm rather than disprove the general rule. Therefore the teaching of the mechanics of continua and, more generally, the maintaining of interest in the mechanics of continua as a unified scientific discipline was, in this period of fragmentation, the job of physicists, who considered it to be a necessary part of a complete course of theoretical physics. So it was not by accident that among those who created courses in mechanics of continua were outstanding physicists: M. Planck, A. Sommerfeld, V. A. Fock, Ya. I. Frenkel, L. D. Landau and E. M. Lifshitz and, more recently, L. M. Brekhovskikh.

The physicists were more interested, however, in general ideas and methods rather than in the consistent presentation of special, even very important, results, which in fact give true shape to the subject.