Study of mathematical models of elastoplastic materials

Abstract

The objective of this article is to study the issues of mathematical elastic-plastic models of a material taking into account the available rheological properties and their connection with the finite element model in modern software complexes of numerical modeling. The article presents the results of numerical modeling of deformation processes of materials, deformation diagrams of materials, analytical methods for approximating deformation diagrams. One of the analytical methods of the restoration of the Prandtl diagram is presented, a method using the Ramberg-Osgood coefficient, which includes the values of reference parameters about the material, such as elastic modulus, tensile strength, yield strength, fracture criteria, elongation and relative thinning. The description and results of numerical modeling of the material destruction, modeling of plastic instability preceding the destruction, and the results of a study to establish grid convergence are presented. The procedure of verifying the numerical model of the material, which is a calibration tests of sample uniaxial rupture model parameters, is given.