The role of mathematics in the development of composite materials mechanics

The paper presents a brief overview of the history of new branches of mathematics and their impact on theoretical studies of mechanics of composite materials. The contribution of Russian and Soviet mathematicians and mechanics is shown, which allowed to create a functional basis for the study of mechanical properties of composites — new materials that have been widely used in engineering and the national economy. Composite materials were created in the second half of the twentieth century. They are multicomponent structures composed of various homogeneous materials. The most common are two-component structures of matrix and filler. Technologically, these components can constitute deterministic or random structures. By changing the structure and properties of the components, it is possible to obtain materials with predetermined macroscopic properties (effective properties) necessary for a particular application. The emergence of composite materials has caused a rapid growth of research on mechanical properties, allowing the design of these materials. These studies were conducted in both theoretical and practical terms. Theoretical studies were mainly reduced to the construction of mathematical models of the mechanical behavior of composites as structurally inhomogeneous materials.