What question did this study set out to answer?

The aim is to explore the mathematical modeling of critical states in heterogeneous plastic strips under load conditions.

June 18, 2026Open Access

Investigation of the Internal Boundary Problem in Models of Critical States of Additively Heterogeneous Joints

Key Points

The aim is to explore the mathematical modeling of critical states in heterogeneous plastic strips under load conditions.
Analyzed a quasi-linear system of hyperbolic equations incorporating equilibrium equations and the Mises plasticity condition.
Utilized approximate methods to find Riemann invariants on characteristics for stress calculations.
Developed analytical expressions for solving the linear conjugation problem at the contact line.
Established analytical expressions for calculating stresses at the contact line.
Successfully solved the internal boundary problem, enhancing understanding of stress behavior in heterogeneous materials.

Abstract

Abstract A mathematical model of the critical state of a heterogeneous plastic strip with a transverse heterogeneous plastic layer in case of plane deformation under a stretchable or compressible load is investigated. This model is a boundary value problem for a quasi-linear system of hyperbolic type equations containing equilibrium equations and the Mises plasticity condition with a variable plasticity parameter. The borders are straight. The ‘‘contact’’ line is orthogonal to the boundary. A linear stress discontinuity condition is set on it. The research method is based on the approximate finding of Riemann invariants on characteristics. This made it possible to find approximate explicit analytical expressions for calculating stresses and, as a result, solve the internal boundary problem (linear conjugation problem) at the contact line between the layer and the base material.

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