EFFECTIVE ELASTIC CONSTANTS OF A FIBER COMPOSITE WITH POROUS MATRIX IN LONGITUDINAL STRETCH - Pozhuev, V. I.; Plechun, V. V.; Spytsia, O. G.; Konchynska, E. O. (Computer Science and Applied Mathematics, 2023)
The problem of mathematical modeling of mechanics characteristics inhomogeneous material’s have been considered in the article. On based of the representative method of volumetric element has been found the analytical relations for the effective longitudinal modulus of elasticity and Poisson’s ratio of a fibrous composite material with a porous matrix. Has been assumed that the porous material matrix’s is isotropic and the fiber material is transtropic. The scheme of reinforcement of the composite material is hexagonal. According to the homogenization procedure, the inhomogeneous material is modeled homogeneous, the mechanical characteristics of which depend on the properties of the components. From the array of composite material stands out a representative volumetric element – a fiber with a surrounding matrix of hexagonal shape. The hexagonal cell is approximated by a cylindrical one. The resulting cylindrical cell consists of two coaxial cylinders – solid, which modeling the fibers, and hollow, which modeling the matrix. To obtain an effective longitudinal modulus of elasticity, two axisymmetric problems for a cylindrical cell have been considered. The first one is about the compatible longitudinal deformation of the porous isotropic matrix and the transtropic fiber. To model the porous properties has been used the known models of porous material, which have been obtained by the method of selfmatching for pores of spherical shape. At the interface between the matrix and the fiber has been assumed perfect adhesion, no leaps of radial displacements and stresses. As a result, has been had all the characteristics of the stress-strain state for such a folded cylindrical cell. Has been solved a similar boundary value problem for a solid cylindrical cell modeling a homogenized transtropic material with unknown elastic characteristics. Comparing the axial displacements of the points of both cylindrical cells allows to obtain analytical relations for the effective elastic longitudinal modulus and Poisson’s ratio of fibrous composite as a function of elastic characteristics of matrix material, material of fiber, matrix porosity and volumetric fiber content in a composite. The influence of porosity on the effective elastic characteristics of the composite material has been analyzed with the help of the obtained analytical relations.