Computer modeling of deformed state of physically non-linear transversal-isotropic bodies with hole

Abstract

The paper presents computer simulation of the deformed state of physically nonlinear transversally isotropic bodies with hole. To describe the anisotropy of the mechanical properties of transversally isotropic materials a structurally phenomenological model is used. This model allows to represent the initial material in the form of two co-operating isotropic materials: the basic material (binder) considered from the positions of continuum mechanics and the fiber material oriented along the anisotropy direction of the original material. It is assumed that the fibers perceive only the axial tensile-compression forces and are deformed together with the base material. To solve the problem of plasticity, a simplified deformation theory of small elastic-plastic deformations for a transversely isotropic body, proposed by prof. Pobedrey B.E., is used. A simplified theory allows to apply the theory of small elastic-plastic deformations to solve specific applied problems, since in this case the fibrous medium is replaced by an equivalent transversely isotropic medium with effective mechanical parameters. The essence of simplification is that with simple stretching of composite in direction of the transversal isotropy axis and in direction perpendicular to it, plastic deformations do not arise. As a result, the intensity of stresses and deformations both along the principal axis of the transversal isotropy and along the perpendicular plane of isotropy is determined separately. The representation of fibrous composites in the form of homogeneous anisotropic materials with effective mechanical parameters makes it possible to make a fairly accurate calculation of stresses and deformations. The calculation is carried out under different loading conditions, bearing in mind that both sizes characterizing the fibrous material-the fiber thickness and the gap between the fibers-are several orders smaller than the radius of the hole. Based on the simplified theory and the finite element method, a computer model of nonlinear deformation of fibrous composites is constructed. For carrying out computational experiments, a specialized software package was developed, the effect of hole configuration on the distribution of deformation and stress fields in the vicinity of concentrators was investigated.