Approaches to modeling the properties of complex structure materials

The approaches to the axiomatic construction of the theoretical basis of continuum\linebreak mechanics are considered. The main notions, laws, hypotheses of the classical theory of\linebreak continuum mechanics and the ways of their modification for non-classic versions of theories are discussed. In the framework of the classical version of the rational theory, the new axioms for the general theory of constitutive relations are proposed. For the media of non-classical type, the approaches to axiomatic construction are studied by the example of the rational mechanics of moment media (Cosserat continuum): the specific notions of bodies with their attributes and the forms of their interactions and motions are introduced, the appropriate generalizations of the main laws and hypotheses are given, the general forms of constitutive relations at arbitrary and at small strains (motions) are analyzed. The approaches to the construction of medium models in accordance with the method of mechanical (constructive) modeling proposed by A.A. Ilyushin are considered.