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

Drawing on forty years of teaching experience, the author presents the basic concepts of mathematical modeling of fluids and solids.

Grigory Isaakovich Barenblatt (Author)

9780521715386, Cambridge University Press

Paperback, published 5 June 2014

273 pages, 110 b/w illus.
24.7 x 17.4 x 1.5 cm, 0.57 kg

'This book achieves clarity of exposition on fringe but important topics that no other book on the market achieves … the legendary author Barenblatt and his groundbreaking lifework are spectacularly immortalized in Flow, Deformation and Fracture.' Colin R. Meyer, Pure and Applied Geophysics

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.

Foreword Alexandre J. Chorin
Preface
Introduction
1. Idealized continuous media: the basic concepts
2. Dimensional analysis and physical similitude
3. The ideal incompressible fluid approximation: general concepts and relations
4. The ideal incompressible fluid approximation: analysis and applications
5. The approximation of a linear elastic solid. Basic equations and boundary value problems of linear theory of elasticity
6. Approximation of a linear elastic body. Applications: brittle and quasi-brittle fracture, strength of structures
7. The approximation of Newtonian viscous fluids: general comments and basic relations
8. Approximation of a Newtonian viscous fluid: the boundary layer
9. Advanced similarity methods: complete and incomplete similarity
10. The ideal gas approximation. Sound waves. Shock waves
11. Turbulence: generalities. Scaling laws for shear flows
12. Turbulence: mathematical models of turbulent shear flows and of the local structure of turbulent flows at very large Reynolds numbers
Bibliography
Index.

Subject Areas: Flow, turbulence, rheology [TGMF3], Mechanics of solids [TGMD], Fluid mechanics [PHDF]