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Abstract <p>In this paper, the formulation of boundary-value problems in perfect plasticity is considered for the stress states corresponding to an edge of the Coulomb-Tresca prism. Solving three-dimensional problems in perfect plasticity requires the formulation of boundary conditions on the surface of a perfectly plastic solid. There are no difficulties in determining the boundary data for the stress tensor in the plane and axisymmetric cases. In three-dimensional case, setting the boundary conditions is associated with solving the problem of determining the orientations of the principal directions of the stress tensor, corresponding to the greatest (or lowest) principal normal stress, on the surface of the solid. It&#xa0;has been shown that, on the free boundary surface, the vector field, indicating the principal directions corresponding to the greatest (or lowest) principal normal stress, is surface-irrotational, and therefore its trajectories are geodesic.</p>

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Boundary Conditions for Three-Dimensional States of Plastic Solids

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Yu. N. Radaev

摘要

Abstract

In this paper, the formulation of boundary-value problems in perfect plasticity is considered for the stress states corresponding to an edge of the Coulomb-Tresca prism. Solving three-dimensional problems in perfect plasticity requires the formulation of boundary conditions on the surface of a perfectly plastic solid. There are no difficulties in determining the boundary data for the stress tensor in the plane and axisymmetric cases. In three-dimensional case, setting the boundary conditions is associated with solving the problem of determining the orientations of the principal directions of the stress tensor, corresponding to the greatest (or lowest) principal normal stress, on the surface of the solid. It has been shown that, on the free boundary surface, the vector field, indicating the principal directions corresponding to the greatest (or lowest) principal normal stress, is surface-irrotational, and therefore its trajectories are geodesic.