ON THE PHYSICO-MATHEMATICAL MODELLING OF THE DETERMINING FUNCTIONAL PROPERTIES AND INTERRELATIONSHIP OF PROPERTIES OF TRADITIONAL AND NANOSTRUCTURAL MATERIALS

Some applied and fundamental problems of the optimal experimental, theoretical, numerical study and prediction of the determining functional properties of various homogeneous and heterogeneous, isotropic and anisotropic materials and nanomaterials are analyzed. The laws of interrelation of properties, dependence on parameters of structure and manufacturing technologies are considered. It is shown that application of separate analytical transformations allows to bring many interrelations to the invariant, not always ideal, s-shaped form reflecting the phase transformations of the structure under impacts. The application efficiency of horizontal and vertical scaling is noted. The experimental data of the author on the uniaxial deformation of polymer samples of a network structure under temperature effects in a wide range are considered. Based on these data, new linear and nonlinear analytical models of the interrelationships of the coefficient of thermal expansion and the coefficient of reduction of the temperature-time correspondence, mechanical and optical compliance, and other defining characteristics of the material are constructed. Universal relationships of the determining properties of other materials in the initial and nanostructured states are noted.