Deformation Model of Spatially Reinforced Fibrous Materials with Physically Nonlinear Matrix

Nonlinear deformation model of spatially reinforced fibrous materials with physically nonlinear matrix has been constructed. The material has been considered as a multi-component system with a random fiber arrangement. The effective deformation properties and stress–strain state of the material have been determined using stochastic differential equations of the physically nonlinear theory of elasticity. Khoroshun’s method of conditional moments has been applied to solve the problem. Algorithms for determining the effective deformation properties of the material have been developed for various cases of spatial reinforcement. The solution to the nonlinear equations, accounting for the physical nonlinearity of the matrix, has been obtained by an iterative method. For each reinforcement case, the relationships between macrostresses and macrostrains have been established, and the stress–strain curves have been plotted.