Approaches to Modeling the Properties of Complex Structure Materials

Abstract

Some approaches to the axiomatic formulation of theoretical fundamentals in continuum mechanics are considered. The basic concepts, laws, and hypotheses in the classical theory of continuum mechanics and their modifications for its nonclassical versions are discussed. In the framework of the classical version of the rational theory, a number of axioms are proposed for the general theory of constitutive relations. For the media of nonclassical type, the approaches to axiomatic formulation are studied by the example of the rational mechanics of moment media (Cosserat continuum): some 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, and the general forms of constitutive relations are analyzed for arbitrary and small strains. The approaches to the construction of medium models are discussed in accordance with the method of mechanical modeling proposed by A. A. Il’yushin.