Mathematical Models of Mediums in Continuum Mechanics

Elements of the theory of constitutive relations. The tangent modulus and the tangent compliance. Physical nonlinearity, tensor linearity (quasilinearity), and nonlinearity. The material functions. Rheonomic and scleronomic media. Homogeneous and inhomogeneous media. Composites. Elastic bodies. Viscous liquids. Media with memory. Non-local media. Tensor functions and their invariants in the theory of constitutive relations. Potential media and conditions of potentiality. Incompressible materials (liquids). Nonlinear elastic-viscoplastic models. Classification of incompressible media (quasilinear models, Bingham bodies, perfectly plastic media, Newtonian viscous fluids). Statement of the linearized boundary value problem of flow stability with respect to small perturbations of the initial data.