Plane Strain State of Composite Material Reinforced by Two Rows of Crystalline Fibres in Dynamic Elastic-Plastic Formulation

Abstract

A generalized approach was developed for solving contact problems in a dynamic elastic-plastic formulation. For the design of composite and reinforced materials, a technique for solving dynamic contact problems in more adequate an elastic-plastic mathematical formulation is used. To consider the physical nonlinearity of the deformation process, the method of successive approximations is used, which makes it possible to reduce the nonlinear problem to a solution of the sequences of linear problems. In contrast to the traditional plane strain, when one normal stress is equal to a certain constant value, for a more accurate description of the deformation of the sample, taking into ac-count the possible increase in longitudinal elongation, we present this normal stress as a function that depends on the parameters that describe the bending of a prismatic body that is in a plain strain state. The problem of a plane strain state of a beam made from the composite reinforced one-layer material is being solved. The reinforced or armed composite material consists of two materials: the main material of glass and two rows of the reinforcing crystalline fourteen fibres of basalt. Glass has high strength and is not affected by the processes of aging of the material, corrosion, and creep. In addition, this material is cheap and widely available. The reinforced composite beam is rigidly linked to an absolutely solid base and on which an absolutely solid impactor acts from above in the centre on a different size of the area of initial contact.