Stress distribution of covering single periodical curved fiber in an infinite elasticity

The curvature of the fibers in the structure of the unidirectional fibrous composite materials is due to design requirements or to technological processes. Usually the curvature caused by the technological process is modeled as a local one, whereas the curvature caused by design features is modeled as a periodical. In this study the case is considered where a covering single periodical curved fiber with an infinite length is contained by an infinite body with low concentration of fibers and stress distribution in that is investigated. Taking the low concentration of fibers into account the interaction between them is neglected. The investigations are carried out within the framework of the piecewise homogeneous body model with the use of the three-dimensional geometrical nonlinear exact equations of the theory of elasticity. There exists the bond hollow covering cylinder between fiber and matrix materials are considered and stresses on interfaces are studied. Moreover it is assumed that the body is loaded at infinity by informally distributed normal forces which act along the fibers and the crosssection of the fibers, normal to its axial line, is a circle of constant radius along the entire fiber length. For the solution of considered boundary value problem an approximate analytical method is developed by using the boundary form perturbation method. The numerous numerical results related to the stress distribution in considered body and the influence of geometrical nonlinearity to this distribution are obtained and interpreted. Moreover, the influences of the geometrical and mechanical problem parameters to these distributions are also analyzed. Keywords: Fibrous composite, stress distribution, geometrical nonlinearity, periodical local curving, covering material, covering single fibrous.