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