THE COMPARATIVE ANALYSIS OF THEORETICAL STUDIES RESULTS OF THE BOUNDARY STRESS STATE OF ANISOTROPIC MATERIALS

Abstract

The purpose of the study is to identify mechanical theories of strength and mathematical models for determining the limiting stress state of anisotropic materials suitable for the adequate description of the elastic range of deformation of softwood and hardwood in biaxial, planar and bulk mechanical loads. The relevance of the study is due to the fact that today there is no unified methodology for approximating the results of experimental studies of the short-term strength of composite materials with a complex stressed state. In the mathematical formulation of the problem, one and the same short-term strength surface can be satisfactorily described by several criteria. To achieve this goal, a classification and a comparative analysis of the known mechanical theories of the short-term strength of anisotropic materials and the main provisions of the general theory of quadrics was made. It has been established that, to date, there is no single generally accepted theory, which methods would adequately assess the limits of elastic, viscoelastic and viscoelastoplastic deformation regions of biological origin anisotropic composite materials under conditions of complex mechanical and temperature-humidity loads. In particular, the strength criteria of Ashkenazi, von Mises, Marin-Hu, Prager, Norris-McKeenen, Hill, Tsai-Hill, Tsai-Wu, Hoffman, Norris, Fisher, Zakharov, Malmeister, and Goldenblat-Kopnov were analysed. As a result, it has been established that the strength conditions for materials with a weak asymmetry of strength limits in the direction of structural symmetry are unsuitable for describing the strength surfaces of materials with a strong asymmetry of ultimate strength. We have revealed that the biaxial and flat stress-strain state in the tangential-radial plane of structural symmetry of hardwood is satisfactorily described by the Ashkenazi criterion and softwood by the Goldenblatt-Kopnov criterion. A promising direction of further research is the identification of a universal strength criterion, suitable, in contrast to the standard tensor-polynomial criteria, to adequately predict the plasticity surface and the region of viscoelastic deformation of anisotropic materials.