岩石非线性细观损伤–塑性耦合本构模型及其数值实现

doi:10.13722/j.cnki.jrme.2023.0634

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摘要为了体现岩石在压缩过程中的压剪破坏模式，解决传统多尺度岩石损伤力学本构模型不能描述剪切弱化的问题，在多尺度岩石损伤力学框架内，通过考虑局部应力Lode角对屈服函数的影响，引入局部莫尔–库仑塑性屈服函数，建立一个新的岩石非线性细观损伤–塑性耦合本构模型。推导出本构模型在常规三轴压缩情况下应力–应变的解析解，进而给出本构模型所有参数的标定方法。采用优化后的半隐式解耦算法将本构模型写入LS-DYNA材料库，通过单元测试验证算法的有效性和收敛性，并对石灰岩三轴压缩力学特性进行模拟，数值模拟结果和试验数据具有较好的一致性。最后，进行本构模型参数敏感性分析，得出模型参数对岩石峰值应力、峰值应变、脆延转变等力学行为的影响规律。所建立的本构模型不需要引入额外的硬化/软化函数，显著减少了模型参数的数量，且参数具有严格的标定方法，采用关联流动法则即可完成对轴向、横向及剪切非线性力学行为的准确描述；优化后的半隐式解耦算法收敛性较好，所编译的LS-DYNA求解器计算过程稳定，且计算速度显著快于岩石传统现象学模型，这对于本构模型的实际应用具有重要意义。

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	张志镇1
	滕业奇1
	周睿2
	张辉3
	徐珂3
	尚晓吉1
	高峰1

关键词 ：岩石力学, 细观力学, 损伤&ndash, 摩擦耦合模型, 局部应力Lode角, 半隐式解耦算法

Abstract：In order to reflect the compressive shear failure mode of rock in the process of compression，and to solve the problem that the original multi-scale rock damage mechanics constitutive model cannot describe the shear weakening，a new nonlinear mesoscopic damage-plastic coupling constitutive model is established in the framework of multi-scale rock damage mechanics by introducing local Mohr-Coulomb plastic yield function. The analytical solution of the constitutive model under conventional triaxial compression is derived，and the calibration method of all parameters of the constitutive model is given. The optimized semi-implicit decoupling algorithm is used to write the constitutive model into LS-DYNA material library，and the convergence and calculation speed of the algorithm are verified by unit test. The triaxial compressive mechanical properties of limestone are simulated by using the proposed meso-mechanical damage model. The numerical simulation results are in good agreement with the experimental data. The influences of the constitutive model parameters on the peak stress，peak strain and brittle-ductile transition of rock are obtained by the sensitivity analysis of constitutive model parameters. The established constitutive model does not need to introduce additional hardening/softening functions，significantly reduces the number of model parameters，and the parameters have a strict calibration method. The correlation flow law can be used to accurately describe the axial，transverse and shear nonlinear mechanical behavior. The convergence of the optimized semi-implicit decoupling algorithm is good，and the calculation process of the compiled LS DYNA solver is stable，and the calculation speed is significantly faster than that of the traditional phenomenological model of rock，which is of great significance for the practical application of the constitutive model.

Key words： rock mechanics micromechanics damage-friction coupling model local stress lode angle semi-implicit decoupling algorithm

引用本文:

张志镇1，滕业奇1，周睿2，张辉3，徐珂3，尚晓吉1，高峰1. 岩石非线性细观损伤–塑性耦合本构模型及其数值实现[J]. 岩石力学与工程学报, 2024, 43(6): 1425-1442.
ZHANG Zhizhen1，TENG Yeqi1，ZHOU Rui2，ZHANG Hui3，XU Ke3，SHANG Xiaoji1，GAO Feng1. Nonlinear mesoscale damage-plasticity coupled constitutive model for rocks and its numerical implementation. , 2024, 43(6): 1425-1442.

链接本文:

http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2023.0634 或 http://rockmech.whrsm.ac.cn/CN/Y2024/V43/I6/1425

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