Kinematics of deformation. Deformation gradient. Deformation measures. Deformation tensor. Homogeneous deformation, dilatation, shear. Deformation of arc, surface and volume elements. Lagrangian and Euler description. Material time derivative. Transport theorems.
Balance laws. Conservation of mass. Balance of linear momentum. Stress tensor. Balance of angular momentum. Cauchy momentum equation. Thermodynamics. Energy and the first law. Entropy and the second law.
Constitutive relations. Material frame indifference. Material symmetry, isotropy. Representation of constitutive functions. Basic models, elasticity, viscoelasticity, plasticity, fluids
Boundary value problem. Variational principles. Stability of the equilibrium. Universal equilibrium solutions.