An Introduction to Continuum Mechanics

by Gurtin

• ISBN13: 9780123097507
• ISBN10: 0123097509
• Format: Hardcover
• Copyright: 1981-11-28
• Publisher: Elsevier Science

Summary

This book presents an introduction to the classical theories of continuum mechanics; in particular, to the theories of ideal, compressible, and viscous fluids, and to the linear and nonlinear theories of elasticity. These theories are important, not only because they are applicable to a majority of the problems in continuum mechanics arising in practice, but because they form a solid base upon which one can readily construct more complex theories of material behavior. Further, although attention is limited to the classical theories, the treatment is modern with a major emphasis on foundations and structure

Table of Contents

Preface	ix
Acknowledgments	xi
Tensor Algebra
Points. Vectors. Tensors	1	(10)
Spectral Theorem. Cayley-Hamilton Theorem. Polar Decomposition Theorem	11	(8)
Selected References	17	(2)
Tensor Analysis
Differentiation	19	(10)
Gradient. Divergence. Curl	29	(8)
The Divergence Theorem. Stokes' Theorem	37	(4)
Selected References	40	(1)
Kinematics
Bodies. Deformations. Strain	41	(13)
Small Deformations	54	(4)
Motions	58	(9)
Types of Motions. Spin. Rate of Stretching	67	(10)
Transport Theorems. Volume. Isochoric Motions	77	(3)
Spin. Circulation. Vorticity	80	(7)
Selected References	85	(2)
Mass. Momentum
Conservation of Mass	87	(5)
Linear and Angular Momentum. Center of Mass	92	(5)
Selected Reference	95	(2)
Force
Force. Stress. Balance of Momentum	97	(11)
Consequences of Momentum Balance	108	(7)
Selected References	113	(2)
Constitutive Assumptions. Inviscid Fluids
Constitutive Assumptions	115	(4)
Ideal Fluids	119	(3)
Steady, Plane, Irrotational Flow of an Ideal Fluid	122	(8)
Elastic Fluids	130	(9)
Selected References	137	(2)
Change in Observer. Invariance of Material Response
Change in Observer	139	(4)
Invariance under a Change in Observer	143	(4)
Selected References	145	(2)
Newtonian Fluids. The Navier-Stokes Equations
Newtonian Fluids	147	(9)
Some Simple Solutions for Plane Steady Flow	156	(3)
Uniqueness and Stability	159	(6)
Selected References	164	(1)
Finite Elasticity
Elastic Bodies	165	(10)
Simple Shear of a Homogeneous and Isotropic Elastic Body	175	(3)
The Piola-Kirchhoff Stress	178	(6)
Hyperelastic Bodies	184	(10)
The Elasticity Tensor	194	(5)
Selected References	198	(1)
Linear Elasticity
Derivation of the Linear Theory	199	(2)
Some Simple Solutions	201	(4)
Linear Elastostatics	205	(9)
Bending and Torsion	214	(6)
Linear Elastodynamics	220	(3)
Progressive Waves	223	(4)
Selected References	226	(1)
Appendix
The Exponential Function	227	(2)
Isotropic Functions	229	(10)
General Scheme of Notation	239	(4)
References	243	(4)
Hints for Selected Exercises	247	(14)
Index	261