CONSTRUCTION OF A MODEL OF NONLINEAR DEFORMATION OF SPATIALLY-REINFORCED FIBER MATERIALS WITH DISORDERED FIBERS

Abstract

A model of nonlinear deformation of fibrous materials of multidirectional reinforcement with misoriented fibers and a physically nonlinear matrix is proposed. A spatially reinforced fibrous material is regarded as a multicomponent material with a random arrangement of fibers. It is based on stochastic differential equations of the physically nonlinear theory of elasticity. The solution to the problem of the stress-strain state and the effective properties of the composite material is constructed by the method of conditional moments of L.P. Khoroshun. An algorithm for determining the effective deformative properties of a spatially reinforced material with a physically nonlinear matrix has been developed. The solution of nonlinear equations taking into account its physical nonlinearity is constructed by an iterative method. The law of connection between macrostresses and macrostrains in a spatially reinforced material and the dependence of average strains and stresses in its matrix on macrostrains have been established. Material deformation curves are plotted for various values of the fiber volumetric content. The dependence of the effective deformative properties of the spatially reinforced material on the volumetric content of fibers has been studied. The influence of the nonlinearity of the matrix on the deformation of a spatially reinforced composite material is investigated. It has been established that the nonlinearity of the matrix has a significant effect on the effective deformative properties and the stress-strain state of spatially reinforced materials.