Continuum Mechanics: Concise Theory and Problems

This comprehensive treatment offers 115 solved problems and exercises to promote understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. Clear, formally precise steps for solving each problem–expressed in a common, efficient notation–foster quick comprehension. 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