Stress return mapping algorithm of Hoek-Brown criterion in principal stress space and its redevelopment

CHEN Pei-shuai; CHEN Wei-zhong; JIA Shan-po; YANG Jian-ping

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Stress return mapping algorithm of Hoek-Brown criterion in principal stress space and its redevelopment

更新时间：2026-06-25

- Stress return mapping algorithm of Hoek-Brown criterion in principal stress space and its redevelopment
- Vol. 32, Issue 7, (2011)
- 作者机构：
  
  1. 中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室,武汉,430071
  2. 长江大学城市建设学院,湖北,荆州,434023
- 作者简介：
- 基金信息：
- DOI：
  CLC： TU45
- Online First：30 June 2011，
  
  Published：2011
- 稿件说明：
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CHEN Pei-shuai, CHEN Wei-zhong, JIA Shan-po, et al. Stress return mapping algorithm of Hoek-Brown criterion in principal stress space and its redevelopment[J]. 2011, 32(7).
DOI：

CHEN Pei-shuai, CHEN Wei-zhong, JIA Shan-po, et al. Stress return mapping algorithm of Hoek-Brown criterion in principal stress space and its redevelopment[J]. 2011, 32(7). DOI：

摘要

在弹塑性模型数值实现的过程中，需要进行应力更新的回映算法。针对三维应力空间回映算法在奇异点收敛性方面的不足，提出主应力空间的回映算法，讨论了算法实现过程的应力空间转化问题，分析了应力更新过程中确定回映区域的方法，建立了相应的一致性刚度矩阵。基于大型有限元软件ABAQUS提供的用户材料子程序UMAT接口，利用 Fortran 编程语言，实现了Hoek-Brown准则主应力空间的隐式积分算法，利用开发的模型，进行了岩石常规三轴压缩试验的数值模拟，通过与ABAQUS内部的Mohr-Coulomb准则计算结果的对比，验证了模型和程序的可行性和准确性

Abstract

In the course of implementing elastoplastic model in the FEM

it is necessary to carry out the process of stress return mapping algorithm. It may be not converging at singular points in three-dimensional space. The transforming method in principal stress space is put forward to overcoming this shortcoming. Also

the process of determining the region of return mapping is analyzed. At last

the consistent stiffness matrix is deduced. Based on the implicit algorithm in principal stress space

the UMAT subroutine of the Hoek-Brown model is developed in ABAQUS with the Fortran programming language. Through the example of triaxial compression test

it is easy to verify the feasibility and accuracy of this method by comparing the result with Mohr-Coulomb criterion in ABAQUS.

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