Definition of the basic problem of mechanics of a rigid deformable body - geometry of the body, method of loading (static x dynamic), type of material. Displacements and deformations, Lagrangian and Eulerian description of motion, displacement gradient, deformation gradient, Jacobian of deformation gradient - volume change, polar decomposition of deformation gradient, Cauchy-Green tensor of deformation, small deformation tensor, its principal directions and principal values, compatibility equation, decomposition of deformation into volume and deviatoric part, other measures of deformation. Internal forces in a solid, Cauchy tensor of real stresses, other stress measures, principal directions and stresses, deviatoric stresses, boundary conditions for stresses. Equations of motion and equilibrium equations for deformable solids, balance of momentum and angular momentum in Cauchy stresses and in some other stress measures. Constitutive equations - relations between stress and strain for linear elastic and thermoelastic solids, isotropic and anisotropic solids, elastic constants, strain energy. Principle of virtual work for deformable solids, principle of minimum def. work, variational formulation of continuum mechanics problems.
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