Continuum Mechanics: Concise Theory and Problems

Table of Contents:
1 VECTOR AND TENSOR THEORY
1 Vector algebra
2 Tensor algebra
3 The tensor product
4 Proper vectors and proper numbers of tensors
5 Symmetric tensors
6 Skew-symmetric tensors
7 Orthogonal tensors
8 Polar decompositions
9 Geometrical consideration: Coordinates
10 "Scalar, vector and tensor fields"
11 Integral theorems
Exercises
2 BASIC KINEMATICS
1 "Bodies, configurations and motions"
2 The referential and spatial descriptions
3 The deformation and velocity gradients
4 Stretch and rotation
5 Stretching and spin
6 Circulation and vorticity
Exercises
3 "BALANCE LAWS, FIELD EQUATIONS AND JUMP CONDITIONS"
1 Mass
2 "Momentum, force and torque"
3 The theory of stress
4 Equations of motion
5 Energy
6 Jump conditions
Exercises
4 CONSTITUTIVE EQUATIONS
1 Basic constitutive statement
2 Examples of constitutive equations
3 Observer transformations
4 Reduced constitutive equations
5 Material symmetry
6 Internal constraints
7 Incompressible Newtonian viscous fluids
8 Isotropic elastic materials
Exercises
Hints and Answers to Exercises
Appendices
Index


Publisher Marketing:

Written in response to the dearth of practical and meaningful textbooks in the field of fundamental continuum mechanics, this comprehensive treatment offers students and instructors an immensely useful tool. Its 115 solved problems and exercises not only provide essential practice but also systematically advance the understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations.
Readers follow clear, formally precise steps through the central ideas of classical and modern continuum mechanics, expressed in a common, efficient notation that fosters quick comprehension and renders these concepts familiar when they reappear in other contexts. Completion of this brief course results in a unified basis for work in fluid dynamics and the mechanics of solid materials, a foundation of particular value to students of mathematics and physics, those studying continuum mechanics at an intermediate or advanced level, and postgraduate students in the applied sciences. "Should be excellent in its intended function as a problem book to accompany a lecture course." -- Quarterly of Applied Math.