Introduction to Continuum Mechanics

Part 1 Introduction: continuum theory; contents of continuum mechanics. Part 2 Tensors: summation convention; dummy indices; Kronecker delta; manipulations with the indicial notation; tensor - a linear transformation; dyadic product of two vectors; the dual vector of an antisymmetric tensor; principal scalar invariants of a tensor; tensor-valued functions of a scalar; curl of a vector field; polar coordinates. Part 3 Kinematics of a continuum: description of motions of a continuum; dilatation; local rigid body displacements; components of deformation tensors in other coordinates. Part 4 Stress: stress vector; equations of motion written with respect to the reference configuration; entropy inequality. Part 5 The elastic solid: mechanical properties; linear elastic solid; reflection of plane elastic waves; stress concentration due to a small circular hole in a plate under tension; constitutive equations for anisotropic elastic solid; constitutive equation for an isotropic elastic solid; change of frame; bending of an incompressible rectangular bar. Part 6 Newtonian viscous fluids: fluids; streamline; pathline; streakline, steady, unsteady, laminar and turbulent flow; irrotational flows as solutions of Navier-Stokes equation; one-dimensional flow of a compressible fluid. Part 7 Integral formulation of general principles: Green's theorem; principle of moment of momentum. Part 8 Non-Newtonian fluids: linear Maxwell fluid; current configuration as reference configuration; special single integral type nonlinear constitutive equations; viscometric flow; answers to problems. (Part contents).