Two-level mathematical models for determining the stress state and life plate with a hole

Abstract

Modern trends in the development of mechanical engineering and other industries related to the production of materials and structures with a given set of physical, mechanical, and technological properties are aimed at reducing material consumption, energy consumption, increasing accuracy, reliability, and competitiveness of the manufactured product. Therefore, the creation of mathematical methods for assessing the stress state of structural elements based on the analysis of the elastic characteristics of a material, taking into account the peculiarities of its internal microstructure, is an actual task. The considered algorithm includes the following stages: identification of strength parameters using data obtained from images of the material microstructure; study of the stress-strain state of the model based on the variational-difference finite element method; formation of a system of linear algebraic equations for solving the problem of analyzing the elastic properties of a material using the plane problem of the theory of elasticity; construction of the material yield surface for a series of tests based on the strength criteria of composite materials, taking into account the different resistance of the material under tensile and compressive loads. Based on the developed mathematical model, the SSS and the yield surface of the plate with a hole are estimated. Structural analysis is performed at the macro and micro levels. The occurrence of plastic deformations at the micro-level can lead to the development of cracks and structural damage at the macro level. As a result of the study, the probability of plastic deformation in the plate is determined, and the critical zones of the model are established. The practical significance of the results obtained is to create an approach to assessing the mechanical properties of a material, such as elastic modulus, shear modulus, Poisson's ratio, and their probabilistic characteristics following the internal material structure. The proposed approach contributes to the expansion of knowledge about the material and allows to increase the valuable information obtained by modeling. To assess the probability of plastic deformations, the generated method uses the entire set of probabilistic characteristics of the yield surface.