DEVELOPMENT OF STATISTICALLY AVERAGED MODELS OF DEFORMATION OF MATERIALS WITH RANDOM NETWORK STRUCTURE OF DIFFERENTLY ORIENTED FIBERS

The paper describes the developed statistically averaged models of deformation of materials with a random network structure of differently oriented fibers. New methods of stress-strain analysis and micromacromechanical models of material deformation in the volume of bodies made of material with a network structure taking into account structural and physical nonlinearities have been created. These models are based on the micromechanics of network structures at the level of statistical sets of their chains. The novelty of approaches, models, methods and results is the creation of theoretical foundations for the analysis of the deformation of non-traditional network materials. Nonlinear mathematical models of material deformation in the form of a chaotic network structure of one-dimensional fragments are proposed, which are constructed involving fundamentally new approaches to the description of physical and mechanical properties at the micro level of statistical sets of fiber chains and spatial homogenization of their macroproperties. Compared to traditional models, they more adequately model the features of material deformation in the form of spatial chaotic and ordered network structures, as they do not involve a number of additional non-physical hypotheses. This creates fundamentally new opportunities not only for analyzing the properties of such materials, but also when creating new ones with specified properties. Using the created methods, models and research tools, the basis for solving a number of model and applied problems has been created. The nature of deformation of non-traditional materials with a network structure of one-dimensional elements is determined. The macro-properties of these materials are established on the basis of the developed micromechanical models, variational formulations and averaging methods. Keywords: stress-strain state, network structures, contact interaction, finite element method, contact pressure, machine parts, variational formulation