Effective properties of composite materials strengthened by orthotropic fibers with regard for the physical nonlinearity of the components

A model of deformation of composite materials with physically nonlinear components is generalized to the case of materials in the form of a matrix reinforced by unidirectional infinite fibers. It is assumed that the matrix is isotropic and deforms nonlinearly and that the fibers are linearly elastic and have orthotropic symmetry. As initial equations, we use the stochastic differential equations of the physically nonlinear theory of elasticity. We transform these equations into integral equations and apply the method of conditional moments. As a result, the problem is reduced to a system of nonlinear algebraic equations solved by the method of simple iterations. On the basis of the proposed approach, we construct algorithms for the evaluation of the effective deformation properties of the composites with orthotropic components in which nonlinearity is caused by the nonlinear deformation of the matrix. We study the dependences of Poisson's ratios on macrostrains, the diagrams of macrodefomation for different volume contents of the components, and the parameters characterizing the shape of the inclusions.
UDC 539.3 Introduction The problem of investigation of the nonlinear deformation properties of composite materials is of great theoretical and practical importance. The nonlinearity of deformation of composite materials can [...]