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Lectures Introduction to continuum mechanics

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 1.1 Vector space, inner product 1.2 Linear transformation . . . . 1.3 Differentiation, gradient . . 1.4 Divergence . . . . . . . . . . . . . . . . . . 2 Kinematics of finite deformation 2.1 Configuration and deformation . 2.2 Strain and rotation . . . . . . . 2.3 Linear strain tensors . . . . . . 2.4 Motions . . . . . . . . . . . . . 2.5 Relative deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 5 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 9 10 11 14 16 3 Balance laws 3.1 General balance equation . . . . . . . . . . 3.2 Local balance equation . . . . . . . . . . . 3.3 Balance equations in reference coordinates 3.4 Conservation of mass . . . . . . . . . . . . 3.5 Equation of motion . . . . . . . . . . . . . 3.6 Conservation of energy . . . . . . . . . . . 3.7 Basic Equations in Material Coordinates . 3.8 Boundary value problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 19 20 20 21 21 23 24 25 . . . . . . . . . . . . . . . 4 Euclidean objectivity 4.1 Frame of reference, observer . . . . . 4.2 Objective tensors . . . . . . . . . . . 4.3 Transformation properties of motion 4.4 Inertial frames . . . . . . . . . . . . . 4.5 Galilean invariance of balance laws .