The Influence of Material Properties, the Geometric Shape of the Section and Temperature on the Stressed State of the Working Bodies

Abstract

In the work on stretching a matrix with a rigid inclusion - an ideal-plastic cylindrical waveguide, a technique was developed for determining the thickness of the boundary layer, which can be generalized and extended to all problems. This research investigates the singular problem of stretching a matrix with a rigid inclusion (ideal-plastic cylindrical waveguide) and proposes a generalized methodology for determining the thickness of the boundary layer under varying loading and geometric conditions. The methodology integrates analytical derivations with computational algorithms, enabling accurate evaluation of boundary layer thickness. The approach is designed for seamless implementation in modern computational mechanics platforms, such as finite e lement analysis (FEA) [20], digital twin systems, and automated engineering design workflows. Numerical simulations validate the method’s accuracy, while potential industrial applications include optimization of composite material reinforcement strategies in fibrous, woven, and laminated systems [23]–[27] and pipeline structural integrity assessment. The work also identifies pathways for experimental validation and integration into digital modelling environments, bridging classical mechanics with contemporary IT, automation, and computational engineering trends.