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.

中文翻译：

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复杂结构材料特性建模的方法

考虑了一些在连续力学中对理论基础进行公理化表达的方法。讨论了连续统力学经典理论中的基本概念，定律和假设及其对非经典形式的修改。在理性理论的经典版本的框架中，为本构关系的一般理论提出了许多公理。对于非经典类型的媒体，通过矩量媒体的理性力学（Cosserat连续体）示例研究公理化表达的方法：介绍一些具有其属性的物体的具体概念以及它们的相互作用和运动形式，适当的给出了主要定律和假设的概括，分析了任意应变和小应变的本构关系的一般形式。根据AA Il'yushin提出的机械建模方法，讨论了构建介质模型的方法。