ME 541 Continuum Mechanics (3-0-0-6)
Introduction to Tensors: Vectors and second order tensors; Tensor operation; Properties of tensors; Invariants, eigenvalues and eigenvectors of second order tensors; Tensor fields; Differentiation of tensors; Divergence, Stokes and Localization theorems.; Kinematics of Deformation: Continuum hypothesis; Deformation mapping; Material (Lagrangian) and Spatial (Eulerian) field descriptions; Length, area and volume elements in deformed configuration; Material and spatial time derivatives - velocity and acceleration; Linearized kinematics; Balance Laws: Conservation of mass; Balance of linear and angular momentum - Cauchy stress tensor, state of stress; Spatial and material forms of balance laws - concept of first and second Piola-Kirchoff stress tensors; Conservation of energy; Continuum Thermodynamics: Basic laws of thermodynamics; Energy equation; Entropy; Clausius-Duhem inequality. Constitutive Equations: Material frame-indifference; Objective stress and stress-rates; Material symmetry; Constitutive relations for Hyperelastic Solids, Generalized Hooke's law; Simple fluids; Navier-Stokes equation.
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