Problem of plane stress state of two-layer body in dynamic elastic-plastic formulation

Abstract

Composite materials are widely used in industry and everyday life. Many different methods are used to calculate and develop composite materials. Many methods of calculation and design of such materials are successfully used. In this article, for the design of composite and reinforced materials, a technique for solving dynamic contact problems in more precise 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. The problem of a plane stress state (PStS) of a beam made from the composite reinforced double-layered material is being solved in dynamic elastic-plastic mathematical model. The reinforced or armed material consists of two layers: the upper (first) thin layer of solid steel and the lower (second) main layer of glass. This composite base is rigidly attached to an absolutely hard half-space. Rigid adhesion of the layers to each other is assumed. Glass is a very strong and very fragile material at the same time. The fragility of glass is due to the fact that there are many microcracks on the surface, and when a load is applied to the glass surface, these microcracks begin to grow and lead to the destruction of glass products. If we glue or immobilize the tops of microcracks on the surface, we will get a strong reinforced armed material that will be lighter, stronger and not subject to degradation of material properties such as aging, corrosion and creep. The impact process was modelled as a non-stationary plane stress state problem with an even distributed load in the contact area, which changes according to a linear law. The fields of the Odquist parameter and normal stresses were studied and compared to corresponding results of plane strain (PSS) problem with the same material of layers, same their thickness and size of the contact area. The upper reinforcing layer of metal or steel can be applied to the glass surface so that metal or steel atoms penetrate deeply, fill microcracks and bind their tops. The top layer can be quite thin.