Flow, Deformation and Fracture : Lectures on Fluid Mechanics and the Mechanics of Deformable Solids for Mathematicians and Physicists

An outstanding resource for every teacher and student of the mechanics of continuous media. The author's unique approach, using the concept of intermediate asymptotics, has been tried and tested over a period of forty years teaching the subject in Russia, Europe and America.

Over forty years of teaching experience are distilled into this text. The guiding principle is the wide use of the concept of intermediate asymptotics, which enables the natural introduction of the modeling of real bodies by continua. Beginning with a detailed explanation of the continuum approximation for the mathematical modeling of the motion and equilibrium of real bodies, the author continues with a general survey of the necessary methods and tools for analyzing models. Next, specific idealized approximations are presented, including ideal incompressible fluids, elastic bodies and Newtonian viscous fluids. The author not only presents general concepts but also devotes chapters to examining significant problems, including turbulence, wave-propagation, defects and cracks, fatigue and fracture. Each of these applications reveals essential information about the particular approximation. The author's tried and tested approach reveals insights that will be valued by every teacher and student of mechanics.