Computational Mathematics

Analysis of critical states of inhomogeneous joints with an indirect contact boundary

V. L. Dilman, A. E. Kashcheeva

South Ural State University, Chelyabinsk, Russian Federation

Abstract: Mathematical models of critical states of discrete heterogeneous joints under conditions of plane deformation are considered. The boundary between sections of different strengths is assumed to be a two-link polyline or contains such a fragment. The purpose of the work is to study the features of the characteristic fields (sliding lines) of such models and to find the stress state at the inner boundary. A characteristic variant of such a field is given; possible locations of stress rupture lines (lines of violation of smoothness of characteristics) and zones of plastic flow in a durable part of the joint are indicated. It has been established how the value of the coefficient of heterogeneity affects the appearance of a plastic section in a durable part of the joint.

Keywords: discretely heterogeneous joints, critical states, stress state, conjugation problem, quasi-linear hyperbolic equations, characteristics.

UDC: 539.374+621.791.052

MSC: 35X20:74C05

Received: 29.11.2025

Language: English

DOI: 10.14529/jcem250402