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Continuum Mechanics

By: A. J. M. SPENCER

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Paperback | 9 April 2004

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192 Pages

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20.9 x 13.6 x 1.3

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The mechanics of fluids and the mechanics of solids represent the two major areas of physics and applied mathematics that meet in continuum mechanics, a field that forms the foundation of civil and mechanical engineering. This unified approach to the teaching of fluid and solid mechanics focuses on the general mechanical principles that apply to all materials. Students who have familiarized themselves with the basic principles can go on to specialize in any of the different branches of continuum mechanics. This text opens with introductory chapters on matrix algebra, vectors and Cartesian tensors, and an analysis of deformation and stress. Succeeding chapters examine the mathematical statements of the laws of conservation of mass, momentum, and energy as well as the formulation of the mechanical constitutive equations for various classes of fluids and solids. In addition to many worked examples, this volume features a graded selection of problems (with answers, where appropriate). Geared toward undergraduate students of applied mathematics, it will also prove valuable to physicists and engineers.

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Non-Fiction Science Physics Classical Mathematics Science in General

Preface
Introduction	p. 1
Continuum mechanics	p. 1
Introductory matrix algebra	p. 4
Matrices	p. 4
The summation convention	p. 6
Eigenvalues and eigenvectors	p. 8
The Cayley-Hamilton theorem	p. 11
The polar decomposition theorem	p. 12
Vectors and cartesian tensors	p. 14
Vectors	p. 14
Coordinate transformations	p. 16
The dyadic product	p. 19
Cartesian tensors	p. 20
Isotropic tensors	p. 22
Multiplication of tensors	p. 23
Tensor and matrix notation	p. 25
Invariants of a second-order tensor	p. 27
Deviatoric tensors	p. 31
Vector and tensor calculus	p. 31
Particle kinematics	p. 33
Bodies and their configurations	p. 33
Displacement and velocity	p. 36
Time rates of change	p. 37
Acceleration	p. 39
Steady motion. Particle paths and streamlines	p. 41
Problems	p. 42
Stress	p. 44
Surface traction	p. 44
Components of stress	p. 45
The traction on any surface	p. 46
Transformation of stress components	p. 49
Equations of equilibrium	p. 51
Principal stress components, principal axes of stress and stress invariants	p. 52
The stress deviator tensor	p. 56
Shear stress	p. 57
Some simple states of stress	p. 57
Problems	p. 60
Motions and deformations	p. 63
Rigid-body motions	p. 63
Extension of a material line element	p. 66
The deformation gradient tensor	p. 68
Finite deformation and strain tensors	p. 70
Some simple finite deformations	p. 74
Infinitesimal strain	p. 78
Infinitesimal rotation	p. 82
The rate-of-deformation tensor	p. 83
The velocity gradient and spin tensors	p. 85
Some simple flows	p. 87
Problems	p. 88
Conservation laws	p. 91
Conservation laws of physics	p. 91
Conservation of mass	p. 91
The material time derivative of a volume integral	p. 96
Conservation of linear momentum	p. 97
Conservation of angular momentum	p. 98
Conservation of energy	p. 100
The principle of virtual work	p. 102
Problems	p. 103
Linear constitutive equations	p. 104
Constitutive equations and ideal materials	p. 104
Material symmetry	p. 106
Linear elasticity	p. 110
Newtonian viscous fluids	p. 116
Linear viscoelasticity	p. 118
Problems	p. 120
Further analysis of finite deformation	p. 123
Deformation of a surface element	p. 123
Decomposition of a deformation	p. 125
Principal stretches and principal axes of deformation	p. 127
Strain invariants	p. 130
Alternative stress measures	p. 132
Problems	p. 134
Non-linear constitutive equations	p. 136
Non-linear theories	p. 136
The theory of finite elastic deformations	p. 136
A non-linear viscous fluid	p. 142
Non-linear viscoelasticity	p. 144
Plasticity	p. 145
Problems	p. 149
Cylindrical and spherical polar coordinates	p. 153
Curvilinear coordinates	p. 153
Cylindrical polar coordinates	p. 153
Spherical polar coordinates	p. 161
Problems	p. 167
Representation theorem for an isotropic tensor function	p. 170
Answers	p. 173
Further reading	p. 179
Index	p. 180
Table of Contents provided by Rittenhouse. All Rights Reserved.

Continuum Mechanics

At a Glance

Paperback

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