Continuum Mechanics

ISBN-10: 0486435946

ISBN-13: 9780486435947

Edition: 2004

Authors: A. J. M. Spencer
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Description: This unified approach to the teaching of fluid and solid mechanics focuses on the general mechanical principles that apply to all materials. It 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. 1992 ed. 23 figures.

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Book details

List price: $17.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 4/9/2004
Binding: Paperback
Pages: 192
Size: 5.75" wide x 8.50" long x 0.50" tall
Weight: 0.440
Language: English

Preface
Introduction
Continuum mechanics
Introductory matrix algebra
Matrices
The summation convention
Eigenvalues and eigenvectors
The Cayley-Hamilton theorem
The polar decomposition theorem
Vectors and cartesian tensors
Vectors
Coordinate transformations
The dyadic product
Cartesian tensors
Isotropic tensors
Multiplication of tensors
Tensor and matrix notation
Invariants of a second-order tensor
Deviatoric tensors
Vector and tensor calculus
Particle kinematics
Bodies and their configurations
Displacement and velocity
Time rates of change
Acceleration
Steady motion. Particle paths and streamlines
Problems
Stress
Surface traction
Components of stress
The traction on any surface
Transformation of stress components
Equations of equilibrium
Principal stress components, principal axes of stress and stress invariants
The stress deviator tensor
Shear stress
Some simple states of stress
Problems
Motions and deformations
Rigid-body motions
Extension of a material line element
The deformation gradient tensor
Finite deformation and strain tensors
Some simple finite deformations
Infinitesimal strain
Infinitesimal rotation
The rate-of-deformation tensor
The velocity gradient and spin tensors
Some simple flows
Problems
Conservation laws
Conservation laws of physics
Conservation of mass
The material time derivative of a volume integral
Conservation of linear momentum
Conservation of angular momentum
Conservation of energy
The principle of virtual work
Problems
Linear constitutive equations
Constitutive equations and ideal materials
Material symmetry
Linear elasticity
Newtonian viscous fluids
Linear viscoelasticity
Problems
Further analysis of finite deformation
Deformation of a surface element
Decomposition of a deformation
Principal stretches and principal axes of deformation
Strain invariants
Alternative stress measures
Problems
Non-linear constitutive equations
Non-linear theories
The theory of finite elastic deformations
A non-linear viscous fluid
Non-linear viscoelasticity
Plasticity
Problems
Cylindrical and spherical polar coordinates
Curvilinear coordinates
Cylindrical polar coordinates
Spherical polar coordinates
Problems
Representation theorem for an isotropic tensor function
Answers
Further reading
Index
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