Lectures "Introduction to continuum mechanics" has contents: Notations and tensor algebra, kinematics of finite deformation, balance laws, euclidean objectivity, principle of material frame-indifference, material symmetry, viscoelastic materials,.and other contents. | Introduction to Continuum Mechanics I-Shih Liu Instituto de Matem´tica a Universidade Federal do Rio de Janeiro 2013 Contents 1 Notations and tensor algebra Vector space, inner product Linear transformation . . . . Differentiation, gradient . . Divergence . . . . . . . . . . . . . . . . . . 2 Kinematics of finite deformation Configuration and deformation . Strain and rotation . . . . . . . Linear strain tensors . . . . . . Motions . . . . . . . . . . . . . Relative deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 5 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 9 10 11 14 16 3 Balance laws General balance equation . . . . . . . . . . Local balance equation . . . . . . . . . . . Balance equations in reference coordinates Conservation of mass . . . . . . . . . . . . Equation of motion . . . . . . . . . . . . . Conservation of energy . . . . . . . . . . . Basic Equations in Material Coordinates . Boundary value problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 19 20 20 21 21 23 24 25 . . . . . . . . . . . . . . . 4 Euclidean objectivity Frame of reference, observer . . . . . Objective tensors . . . . . . . . . . . Transformation properties of motion Inertial frames . . . . . . . . . . . . . Galilean invariance of balance laws .
