ЧИСЕЛЬНЕ ВИЗНАЧЕННЯ ЕФЕКТИВНИХ ПРУЖНИХ ХАРАКТЕРИСТИК ТРИВИМІРНОАРМОВАНОГО ВОЛОКНИСТОГО КОМПОЗИЦІЙНОГО МАТЕРІАЛУ

Abstract

The processes occurring in composite materials are determined by differential equations in partial derivatives with variable coefficients. Most composite materials have a periodic structure, so the coefficients in the equations are rapidly oscillatory periodic functions. The most effective method for studying the stress and deformation field in structures made of composite materials is the method of finite elements, where a nonhomogeneous composite material is replaced by an equivalent homogeneous anisotropic material. To determine averaged characteristics of a composite material with a periodic structure requires a verified methodology allowing to do this. Therefore, the fundamental goal of the mechanics of composite materials is to calculate the effective elastic characteristics of the material. The paper considers the urgent issue of determining effective elastic characteristics of three-dimensional reinforced composite materials based on known elastic properties of fibers and matrix and distribution of reinforcing fibers by volume of composite material.The paper presents the mathematical modeling of the minimum three-dimensional representative volume element based on the specified reinforcement scheme and geometrical dimensions of components. Numerical experiments are performed with the ANSYS software package. A series of numerical experiments simulate six deformation cases: uniaxial tension in the X, Y, Z directions, and shear in the XY, YZ, and XZ planes. Numerical studies of the stress and strain state of the representative volume element of composite material determine the effective elastic constants of equivalent homogeneous material. Two series of calculations are performed with specifying appropriate symmetry and periodicity conditions.The results of the experimental study allow for the verification of the proposed methodology for determining the effective elastic characteristics of three-dimensional reinforced fiber composite materials. The developed numerical methodology enables us to solve the issues of the mechanics of composite materials with the help of modern software packages in the mathematical framework of which the finite element method is used.