Dekret V. Three-dimensional Theory of Stability of Composite Materials Reinforced by Short Fibers. The Plane Strain Model

In the Thesis based on the three-dimensional linearized theory of stability of deformable bodies developed the theory of stability of composite materials reinforced by short fibers. The model of "finite size fibers" allows taking into account the finite size of the reinforcing elements under the plane strain conditions. The strict mathematical formulation of the problem has been performed using the three-dimensional linearized theory of stability of deformable bodies in the framework of the piecewise homogeneous medium. The method of constructing of the discrete problems using the method of finite differences and the software technology automate construction of discrete models have been developed and the numerical solutions have been obtained. The solution results have been obtained for the composite materials stability problems for the following cases: one and two short fibers, periodic series of short fibers, and the case of short fibers near the free boundary surface. The influence of mechanical and geometrical parameters of the composite components on the critical strain and buckling of reinforcing elements in the composite structure has been investigated.