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<p>To achieve a close physical approximation to the singular yield and plastic potential surfaces given by the Tresca and Mohr–Coulomb criteria, this paper introduces new rounding techniques using circular cylinders and cones to smooth their edges. A formula is also provided to quantify the deviation from the original yield surface. In contrast to the von Mises and Owen rounding methods, the proposed approach slightly underestimates material strength, thereby offering a conservative estimate. Using the Mohr–Coulomb model, 2D and 3D user material subroutines were developed in Abaqus, employing a backward Euler integration algorithm to update the stress upon yielding. The reliability and effectiveness of the user material subroutines were verified through numerical simulations of triaxial compression and uniaxial tension tests. Comparative analyses with Abaqus’s built-in Mohr–Coulomb model and the Abbo–Sloan method demonstrate the advantages of the proposed technique.</p>

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Rounding Approaches on Singular Yield and Plastic Potential Surfaces Using Circular Cylinders or Cones

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Xiang Xu,
  • Hua Zhong,
  • Rui Dai

摘要

To achieve a close physical approximation to the singular yield and plastic potential surfaces given by the Tresca and Mohr–Coulomb criteria, this paper introduces new rounding techniques using circular cylinders and cones to smooth their edges. A formula is also provided to quantify the deviation from the original yield surface. In contrast to the von Mises and Owen rounding methods, the proposed approach slightly underestimates material strength, thereby offering a conservative estimate. Using the Mohr–Coulomb model, 2D and 3D user material subroutines were developed in Abaqus, employing a backward Euler integration algorithm to update the stress upon yielding. The reliability and effectiveness of the user material subroutines were verified through numerical simulations of triaxial compression and uniaxial tension tests. Comparative analyses with Abaqus’s built-in Mohr–Coulomb model and the Abbo–Sloan method demonstrate the advantages of the proposed technique.