Mathematical modeling of the stress-strain state in metallic media based on the concept of force lines

Abstract

In this article, based on the classical works of G. Kirsch, K. Inglis, G.~V.~Kolosov, and N.~I.~Muskhelishvili, we continue to develop a mathematical apparatus that allows us to obtain solutions to a number of three-dimensional problems of fracture mechanics in a hardened metal medium.

Based on the work of G.~R.~Irwin, G.~I.~Barenblatt, Westergaard, L.~D.~Landau, and E.~M.~Livshits, the authors performed mathematical modeling of the stress-strain state in the volume of a loaded steel sample in the vicinity of pores of various morphologies resulting from operational loads and aggressive environmental influences. An algorithm for determining the components of the stress tensor near concentrators in the form of pores of various shapes is proposed for understanding the force lines of the stress field in a metallic medium. A stationary case with a fixed ratio of external stress and yield strength was considered.