# Flow, Deformation and Fracture: Lectures on Fluid Mechanics and the Mechanics of Deformable Solids for Mathematicians and Physicists: 49 (Cambridge Texts in Applied Mathematics, Series Number 49)

Cambridge University Press, 6/5/2014

EAN 9780521715386, ISBN10: 0521715385

Paperback, 273 pages, 24.6 x 17.5 x 1.5 cm

Language: English

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.

'Now those not fortunate enough to have been able to attend the course have the opportunity to see what has made it so special. The present book is a masterful exposition of fluid and solid mechanics, informed by the ideas of scaling and intermediate asymptotics, a methodology and point of view of which Professor Barenblatt is one of the originators ... This is indeed a remarkable book.' Alexandre J. Chorin, from the Foreword