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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 [...]

The theory of long-term damageability of a homogeneous material is generalized to the case of an orthotropic fibrous composite material with a stochastic structure. Equations of mechanics of microinho-mogeneous media of this structure form the base of the theory. The process of damage of components of a composite is modeled by the formation of stochastically located micropores. The criterion of fracture of a unit microvolume is characterized by its long-term strength determined by the dependence of the time of brittle fracture on the degree of closeness of the equivalent stress to its limit value, which characterizes the short-term strength on the basis of the Huber-von Mises criterion accepted as an arbitrary function of coordinates. Efficient deformation properties and the stress-strain state of an orthotropic fibrous composite with microdamages in components are determined on the base of stochastic equations of elasticity of orthotropic media. For given macrostresses and macrostrains and an arbitrary moment of time, balance equations of damage (porosity) of components are formulated. On the basis of the iteration method, we construct algorithms for calculating dependences of microdamage of components of an orthotropic fibrous material on time and dependences of macrostresses or macrostrains on time and obtain the corresponding curves for the case of a bounded function of the long-term microstrength, which is approximated by an exponential law. UDC 539.3, 1. Introduction One of possible mechanisms of fracture of materials and structural elements is connected with the occurrence and development of dispersed microdamages with time, which, as a rule, lead [...]

In the present work, a model of nonlinear deformation of stochastic composites under microdamaging is developed for the case of a composite with orthotropic inclusions, when microdefects are accumulated in the matrix. The composite is treated as an isotropic matrix strengthened by triaxial arbitrarily oriented ellipsoidal inclusions with orthotropic symmetry of the elastic properties. It is assumed that the process of loading leads to accumulation of damage in the matrix. Fractured microvolumes are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining the effective elastic modules in the case of orthotropic components are taken as basic relations. The fracture criterion is specified as the limiting value of the intensity of average shear stresses acting in the intact part of the material. On the basis of the analytic and numerical approach, we propose an algorithm for the determination of nonlinear deformation properties of the investigated material. The nonlinearity of composite deformations is caused by the finiteness of deformations. By using the numerical solution, the nonlinear stress-strain diagrams are predicted and discussed for an orthotropic composite material for various cases of orientation of inclusions in the matrix. UDC 539.3, 1. Introduction The problem of behavior of composite materials under the action of high loads is of significant theoretical interest and, at the same time, actual and important for various [...]