Syllabus
* Strain
Reference and present configurations, Lagrangian and Eulerian descriptions of deformation, base vectors, shifters, axiom of continuity, deformation gradients and tensors, polar decomposition of deformation gradient, Jacobi's identities, displacement vector, length and angle changes, strain invariants and principal directions, area and volume changes, changes of an external normal, compatibility conditions, geometrical linearization, small deformations, orthogonal curvilinear coordinates.
* Kinematics
Material and spatial time derivatives, material derivative of surface and volume integrals, Reynolds' transport theorem.
* Stress
External and internal loads, volume and surface forces, Cauchy traction principle, Cauchy stress tensor, Cauchy stress formula, Piola-Kirchhoff stress tensors.
* Fundamental axioms of Continuum Mechanics
Conservation of mass, balance of linear momentum, balance of angular momentum, conservation of energy, entropy inequality, local balance laws, jump and boundary conditions, local balance laws in the reference frame, interface and boundary conditions, Lagrangian and Eulerian form of Poisson's equation.
* Classical linear elasticity
Anisotropic linear elastic solids, Hooke's law for isotropic solids, Lamé parameters, restriction on elastic coefficients, the equation of motion in anisotropic and isotropic medium, deformation of elastic plate by its own weight.
* Fluid dynamics
Constitutive equations, Newtonian and Stokesian fluids, thermodynamic and hydrostatic pressures, experimental origin of viscosity, the Navier-Stokes equation, boundary conditions.
Annotation
Deformation, deformation tensors, polar decomposition, volume and area deformation, geometric linearization.
Kinematics, material time derivative, Reynold's theorem. Surface and volume forces, Cauchy traction principle, stress tensors. Basic axioms, mass conservation, balance of linear momentum and angular momentum, energy conservation. Integral and differential forms. Interface conditions. Classical linear elasticity. Fluid dynamics.