基于改进后光滑GZZ准则的弹塑性本构模型在ABAQUS中的数值实现

doi:10.3724/1000-6915.jrme.2024.0575

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摘要光滑GZZ(Smoothed Zhang-Zhu)准则是近年提出的岩石三维强度准则，可以合理可靠地描述岩石材料的非线性强度特征。然而，仅有少数有限元软件配备了这一准则，且现有基于GZZ准则的本构模型程序大多在主应力空间进行，在ABAQUS中应用困难。此外，目前基于光滑GZZ准则的数值模拟往往使用关联理想弹塑性模型，忽略了岩石的塑性变形特性和强度非线性。本文改进光滑GZZ准则的塑性势函数，提出基于光滑GZZ准则的本构模型在一般应力空间的数值实现方法，避免主应力转化问题；同时，给出考虑岩石膨胀特性和强度变化的计算方法。最后通过在ABAQUS中编写UMAT子程序实现这一本构模型的计算。经3个算例验证，该模型可直接在一般应力空间进行计算，能体现岩石膨胀特性、强度非线性，数值解与解析解和模型试验结果吻合，具有较高的计算精度。

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	武文杰1
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	朱合华1
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关键词 ：岩石力学, GZZ强度准则, 本构模型, 回归映射方法, 数值模拟

Abstract：The Smoothed Zhang-Zhu(GZZ) criterion is a three-dimensional strength criterion for rocks proposed in recent years，which can reasonably and reliably describe the nonlinear strength characteristics of rock materials. However，only a few finite element software are equipped with this criterion，and most of the existing constitutive model programs based on the GZZ criterion are carried out in the principal stress space，making it difficult to apply in ABAQUS. In addition，the current numerical simulations based on the Smoothed GZZ criterion often use the associated ideal elastoplastic model，ignoring the plastic deformation characteristics and strength nonlinearity of rocks. In this paper，the plastic potential function of the Smoothed GZZ criterion is improved，and a numerical implementation method of the constitutive model based on the Smoothed GZZ criterion in the general stress space is proposed to avoid the problem of principal stress transformation. Meanwhile，a calculation method considering the dilation characteristics and strength variation of rocks is given. Finally，the calculation of this constitutive model is implemented by writing a UMAT subroutine in ABAQUS. Verified by three calculation examples，this model can directly conduct calculations in the general stress space，can reflect the dilation characteristics and strength nonlinearity of rocks，and the numerical solutions are in good agreement with the analytical solutions and the results of model tests，showing a relatively high calculation accuracy.

Key words： rock mechanics the GZZ criterion constitutive model return mapping algorithm numerical simulation

引用本文:

武文杰1，武威1，2，邹育麟3，古浩4，朱合华1，2. 基于改进后光滑GZZ准则的弹塑性本构模型在ABAQUS中的数值实现[J]. 岩石力学与工程学报, 2025, 44(4): 1001-1012.
WU Wenjie1，WU Wei1，2，ZOU Yulin3，GU Hao4，ZHU Hehua1，2. Numerical implementation of the elastoplastic constitutive model based on the improved smoothed GZZ criterion into ABAQUS. , 2025, 44(4): 1001-1012.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2024.0575 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I4/1001

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