LONGITUDINAL EFFICIENT MODULE OF ELASTICITY OF FIBER COMPOSITE MATERIAL UNDER NONLINEAR DEFORMATION CONDITIONS

Abstract

The article considers mathematical modeling of the mechanical behavior of a fibrous composite to determine its stress-strain state under nonlinear deformation. Analytical relations were found for the effective characteristics of the fibrous composite material, namely the modulus of elasticity and Poisson’s ratio, taking into account the isotropic properties of the matrix and fiber. The method of representative three-dimensional element is used to determine the effective characteristics. The joint deformation of the hollow and solid cylinders, which simulate, respectively, the matrix and the fiber in the composite, taking into account the fact that the axial displacements and the fiber matrix have become the same. It is believed that in the process of deformation both the matrix material and the fibrous material obey Hooke’s law, but in the process of deformation their volume fraction in the composite changes. In addition, this change will be determined by the change in the cross-sectional area of the units of the unit cell occupied by the matrix and the fiber, given that the height of the infinite cell will be the same for the matrix and the fiber. The relations for the stress-strain state of the isotropic fiber and the matrix are obtained. In which it is assumed that despite the linear nature of the deformation of the matrix and the fiber, the volume fraction of the components changes with increasing external load and as a result we will have a nonlinear dependence. Next, a similar problem is considered for a homogeneous transversely isotropic material that simulates the behavior of a composite material. The condition of agreement for this problem will be the equality of axial displacements for an arbitrary axial coordinate and the equality of radial displacements on the outer part of the cylindrical surface. The formula for determining the longitudinal modulus of elasticity of a composite material with isotropic matrix and fiber is obtained. The dependence of the modulus of elasticity and Poisson’s ratio on the change in the volumetric content of the fiber in the composite during deformation has been studied.