HOMOGENIZATION OF A TRANSTROPIC COMPOSITE WITH RANDOM PARAMETERS OF A HOLLOW FIBER

When designing structures made of composite materials, a composite model is used in practice as a continuous homogeneous medium. Its physical and mechanical properties as a homogeneous material reflect the effective constants. Of course, the parameters of the components of the composite are random variables. Therefore, its effective constants are also random variables.In this regard, the actual task is to homogenize the composite taking into account the stochasticity of its parameters, including the determination of the characteristics of elastic constants as random variables.In the work, the object of research is a unidirectional fiber composite, the phases of which are a transversal-isotropic matrix and hollow fiber. The radius of the fiber and the cavity in it are modeled as random variables with a normal distribution law. Accordingly, the effective parameters of the composite are also random variables. The method of determining the mathematical expectation of an effective longitudinal modulus of elasticity, which can be used to find other numerical characteristics of effective parameters as functions of random variables, is proposed.To solve the homogenization problem, the composite is modeled by a continuous homogeneous transversal-isotropic material. The conditions of perfect bonding are fulfilled at the contact surface between the matrix and the fiber. As result of the research, a formula was obtained for the effective longitudinal modulus of elasticity as a function of random variables. The volume fractions of the fiber and the cavity in the fiber for the composite are random. The distribution densities of these random variables are found. The elastic constants of the fiber and matrix are considered as deterministic variables. The obtained expression of the effective longitudinal modulus of elasticity as a function of random variables allowed us to determine its characteristics – mathematical expectation and variance. The obtained distribution densities of random arguments can be used to determine other moments of this random variable.The proposed method can be used to solve the problem of homogenization of composites, the phases of which have random characteristics with other continuous distributions different from the normal one.