This paper proposes a modified return mapping algorithm for a series of nonlinear yield criteria. The algorithm is established in the principal stress space and ignores the effect of the intermediate principal stress. Three stress return schemes are derived in this paper: return to the yield surface, return to the curve, and return to the apex point. The conditions used for determining the correct stress return type are also constructed. After the proposed algorithm is programmed in the finite element software, we merely need the equivalent Mohr–Coulomb (M-C) strength parameters, the derivatives of their functions, and the tensile strength of these nonlinear yield criteria. In addition, the Hoek–Brown (H-B) yield criterion is taken as an example to validate the proposed method. The results show that the updated stresses and the final principal stresses obtained by the proposed method are in good agreement with those obtained by other methods. Furthermore, the proposed method is more suitable for the associated plastic-flow rule.

中文翻译：

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等效Mohr-Coulomb强度参数的非线性屈服准则的返回映射算法

针对一系列非线性屈服准则，提出了一种改进的收益映射算法。该算法建立在主应力空间中，并且忽略了中间主应力的影响。本文推导了三种应力返回方案：返回到屈服面，返回到曲线以及返回到顶点。还确定了用于确定正确的应力返回类型的条件。在有限元软件中对提出的算法进行编程后，我们只需要等效的Mohr-Coulomb（MC）强度参数，其函数的导数以及这些非线性屈服准则的抗拉强度。另外，以Hoek-Brown（HB）屈服准则为例来验证所提出的方法。结果表明，所提方法获得的更新应力和最终主应力与其他方法所获得的吻合良好。此外，所提出的方法更适合于相关的塑性流动规则。