Nonlinear Deformation Properties of Composites with Transversely Isotropic Components

The deformation model of composite materials with physically nonlinear components is generalized to materials reinforced with unidirectional spheroidal inclusions. It is assumed that the matrix is isotropic and described by a nonlinear stress–strain curve and the inclusions are transversely isotropic and linear elastic. The stochastic differential equations of the physically nonlinear theory of elasticity are reduced to integral equations, which are then reduced by the method of conditional moments to a system of algebraic equations solved by the simple iteration method. The proposed approach underlies algorithms developed to evaluate the effective elastic properties of composites with transversely isotropic components when nonlinearity is due to the nonlinear deformation of the matrix. The dependence of Poisson’s ratios on macrostrains and the macrostress–macrostrain curves for different volume fractions of components and different shapes of inclusions are analyzed