Анализ реакции волоконных материалов на действие нагрузок на основе микромеханических моделей

Abstract

The work proposes nonlinear physical and mathematical models based on fiber materials micro mechanics down to the level of statistical ensembles of segments. The main purpose is analysis of the deformed state of engineering structures composed of such materials. The theoretical grounds to the proposed approach included methods of solid mechanics, in particular the general formulation of the state equations. The nonlinear relations describing physico-mechanical properties of polymer materials are derived by means of the special statistical theory of fiber network micro mechanics. New variational formulations are derived from the variational principles. They can be used to determine mechanical response of fiber-based material to finite deformations with account for the loading history. The irreversible mechanisms treated by the proposed approach included inter-fiber friction resulting in their relative sliding. Furthermore model homogenization has been proposed for these fibrous materials. It is distinguished by an averaging procedure that relies on integration in the representative orientation space. This allows effective transition from the microscopic model to the macroscopic properties of the material. As a result new, more adequate nonlinear material models based on the novel approach to the statistical homogenization of materials micro stucture are developed. They provide useful micro mechanical explanation of the peculiar properties of such materials and can quantitatively accurately determine their behavior under mechanical load. Besides the analysis of the existing materials it is possible to predict mechanical properties of the newly developed materials based on these theoretical grounds. This information is crucial in light of the high-performance tailored materials.