Stress concentration in a generalized elasto-plastic medium

D. S. Zhurkina, S. V. Lavrikov, A. F. Revuzhenko

Institute of Mining, Siberian Branch of the Russian Academy of Sciences

Abstract: This paper proposes a mathematical model within the class of generalized continua that account for an internal microstructure. The model considers the inhomogeneous deformation of an infinitesimal volume element. It incorporates plastic slips at the interfaces between these volume elements. Unlike classical continuum mechanics, the formulation introduces additional kinematic degrees of freedom. In the planar case, these are represented by two independent smooth displacement fields, which introduce a length-scale parameter into the constitutive equations, characterizing the internal structure of the medium. The model is applied to numerically solve the problem of stress redistribution in the near-field zone of a system of mine excavations in a rock mass, induced by a specific mineral extraction technology. The results demonstrate that accounting for the material microstructure, which is a feature absent in classical elastoplastic models, shifts a significant portion of the load from the excavation boundaries deeper into the rock mass.

Keywords: mathematical model, structure, plastic slip, rock mass, excavation, stress redistribution.

UDC: 539.3+622.83

Received: 29.05.2025
Revised: 15.06.2025
Accepted: 23.06.2025

DOI: 10.15372/PMTF202515668

 English version: Journal of Applied Mechanics and Technical Physics, 2025, 66:5, 987–997

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