基于相场方法的岩石弹塑性损伤模型研究及其数值实现

doi:10.13722/j.cnki.jrme.2022.0540

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摘要岩石材料损伤破坏的研究对岩体工程的稳定性评价至关重要，基于热力学原理，在经典相场损伤模型框架中引入塑性本构模型和硬化准则，借助塑性耗散能驱动下的塑性硬化阶段和峰后软化阶段损伤演化方程，建立一种岩石弹塑性相场损伤模型，并给出其数值实现。通过对比相场损伤均质响应模拟结果和解析解，验证塑性损伤耦合条件下该模型的正确性和可靠性。采用该模型，模拟岩石二维和三维复杂裂纹扩展，研究含预制裂纹岩石试样的塑性剪切损伤破坏过程，计算结果与已有试验结果吻合较好。该模型能自动、准确地跟踪岩石复杂裂纹扩展路径，有效描述岩石的损伤演化规律以及塑性变形与非局部相场损伤之间的耦合效应，可进一步应用到模拟实际工程岩石损伤破坏及稳定性问题。

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	刘世藩1
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	王伟1
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	曹亚军1
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	朱其志1
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	邵建富1
	2
	3

关键词 ：岩石力学, 相场模型, 损伤演化, 塑性损伤耦合, 裂纹扩展

Abstract：The study of damage and failure of rock is of vital significance in the stability evaluation of rock engineering. Based on thermodynamic principles，the plastic constitutive model and hardening law are introduced into the framework of classical phase-field damage model. The damage evolution equation is driven by the plastic dissipation energy，during the plastic hardening stage and post-peak softening stage. In this way，a novel elastoplastic phase-field damage model for rock is established and its numerical implementation is given. The simulation results and analytical solutions of the phase-field homogeneous response are compared. The accuracy and reliability of the model under the plastic-damage coupling effects are verified. Then，two-dimensional and three-dimensional crack propagation in rock is simulated by the proposed model. The plastic shear damage and failure process of rock samples with pre-existing notches are studied. The simulation results are in good agreement with the existing experimental observations. By means of the proposed model，the complex propagation path of cracks in rock can be automatically and accurately tracked. Meanwhile，the damage evolution law of rock and the coupling effects between plastic deformation and non-local phase-field can be effectively described. The model can be further applied to simulate the damage failure and analyze the stability of rock in practical engineering.

Key words： rock mechanics phase-field model damage evolution plasticity-damage coupling crack propagation

引用本文:

刘世藩1，2，王伟1，2，曹亚军1，2，朱其志1，2，邵建富1，2，3 . 基于相场方法的岩石弹塑性损伤模型研究及其数值实现[J]. 岩石力学与工程学报, 2023, 42(4): 896-905.
LIU Shifan1，2，WANG Wei1，2，CAO Yajun1，2，ZHU Qizhi1，2，SHAO Jianfu1，2，3. Study on the elastoplastic damage model for rock based on the phase-field method and its numerical implementation. , 2023, 42(4): 896-905.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2022.0540 或 https://rockmech.whrsm.ac.cn/CN/Y2023/V42/I4/896

[1] 朱其志. 多尺度岩石损伤力学[M]. 北京：科学出版社，2019：6–11.(ZHU Qizhi. Multiscale rock damage mechanics[M]. Beijing：Science Press，2019：6–11.(in Chinese))
[2] AMOR H，MARIGO J J，MAURINI C. Regularized formulation of the variational brittle fracture with unilateral contact：numerical experiments[J]. Journal of the Mechanics and Physics of Solids，2009，57(8)：1 209–1 229.
[3] KUHN C，MÜLLER R. A continuum phase field model for fracture[J]. Engineering Fracture Mechanics，2010，77(18)：3 625–3 634.
[4] VERHOOSEL C V，DE BORST R. A phase-field model for cohesive fracture[J]. International Journal for numerical methods in Engineering，2013，96(1)：43–62.
[5] MARTÍNEZ-PAÑEDA E，GOLAHMAR A，NIORDSON C F. A phase field formulation for hydrogen assisted cracking[J]. Computer Methods in Applied Mechanics and Engineering，2018，342：742–761.
[6] ZHOU S，ZHUANG X，RABCZUK T. A phase-field modeling approach of fracture propagation in poroelastic media[J]. Engineering Geology，2018，240：189–203.
[7] 刘国威，李庆斌，左正. 相场断裂模型分步算法在ABAQUS中的实现[J]. 岩石力学与工程学报，2016，35(5)：1 019–1 030.(LIU Guowei，LI Qingbin，ZUO Zheng. Implementation of a staggered algorithm for a phase field model in ABAQUS[J]. Chinese Journal of Rock Mechanics and Engineering，2016，35(5)：1 019–1 030.(in Chinese))
[8] FRANCFORT G A，MARIGO J J. Revisiting brittle fracture as an energy minimization problem[J]. Journal of the Mechanics and Physics of Solids，1998，46(8)：1 319–1 342.
[9] BOURDIN B，FRANCFORT G A，MARIGO J J. Numerical experiments in revisited brittle fracture[J]. Journal of the Mechanics and Physics of Solids，2000，48(4)：797–826.
[10] MIEHE C，WELSCHINGER F，HOFACKER M. Thermodynamically consistent phase-field models of fracture：Variational principles and multi-field FE implementations[J]. International Journal for Numerical Methods in Engineering，2010，83(10)：1 273–1 311.
[11] WU J Y. A unified phase-field theory for the mechanics of damage and quasi-brittle failure[J]. Journal of the Mechanics and Physics of Solids，2017，103：72–99.
[12] 吴建营. 固体结构损伤破坏统一相场理论，算法和应用[J]. 力学学报，2021，53(2)：301–329.(WU Jianying. On the theoretical and numerical aspects of the unified phase-field theory for damage and failure in solids and structures[J]. Chinese Journal of Theoretical and Applied Mechanics，2021，53(2)：301–329.(in Chinese))
[13] BYERLEE J D. Brittle-ductile transition in rocks[J]. Journal of Geophysical Research，1968，73(14)：4 741–4 750.
[14] DUDA F P，CIARBONETTI A，SÁNCHEZ P J，et al. A phase-field/ gradient damage model for brittle fracture in elastic-plastic solids[J]. International Journal of Plasticity，2015，65：269–296.
[15] AMBATI M，GERASIMOV T，DE LORENZIS L. Phase-field modeling of ductile fracture[J]. Computational Mechanics，2015，55(5)：1 017–1 040.
[16] BORDEN M J，HUGHES T J R，LANDIS C M，et al. A phase-field formulation for fracture in ductile materials：Finite deformation balance law derivation，plastic degradation，and stress triaxiality effects[J]. Computer Methods in Applied Mechanics and Engineering，2016，312：130–166.
[17] ALESSI R，MARIGO J J，MAURINI C，et al. Coupling damage and plasticity for a phase-field regularisation of brittle，cohesive and ductile fracture：one-dimensional examples[J]. International Journal of Mechanical Sciences，2018，149：559–576.
[18] FANG J，WU C，RABCZUK T，et al. Phase field fracture in elasto-plastic solids：Abaqus implementation and case studies[J]. Theoretical and Applied Fracture Mechanics，2019，103：102252.
[19] CHOO J，SUN W C. Coupled phase-field and plasticity modeling of geological materials：From brittle fracture to ductile flow[J]. Computer Methods in Applied Mechanics and Engineering，2018，330：1–32.
[20] KIENLE D，ALDAKHEEL F，KEIP M A. A finite-strain phase-field approach to ductile failure of frictional materials[J]. International Journal of Solids and Structures，2019，172：147–162.
[21] YOU T，WAISMAN H，ZHU Q Z. Brittle-ductile failure transition in geomaterials modeled by a modified phase-field method with a varying damage-driving energy coefficient[J]. International Journal of Plasticity，2021，136：102836.
[22] YOU T，WAISMAN H，CHEN W Z，et al. A novel micromechanics- enhanced phase-field model for frictional damage and fracture of quasi-brittle geomaterials[J]. Computer Methods in Applied Mechanics and Engineering，2021，385：114060.
[23] MIEHE C，HOFACKER M，WELSCHINGER F. A phase field model for rate-independent crack propagation：Robust algorithmic implementation based on operator splits[J]. Computer Methods in Applied Mechanics and Engineering，2010，199(45–48)：2 765–2 778.
[24] YU Z，SHAO J F，VU M N，et al. Numerical study of thermo-hydro-mechanical responses of in situ heating test with phase-field model[J]. International Journal of Rock Mechanics and Mining Sciences，2021，138：104542.
[25] ZHANG X，SLOAN S W，VIGNES C，et al. A modification of the phase-field model for mixed mode crack propagation in rock-like materials[J]. Computer Methods in Applied Mechanics and Engineering，2017，322：123–136.
[26] GERASIMOV T，DE LORENZIS L. A line search assisted monolithic approach for phase-field computing of brittle fracture[J]. Computer Methods in Applied Mechanics and Engineering，2016，312：276–303.
[27] INGRAFFEA A R，HEUZE F E. Finite element models for rock fracture mechanics[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1980，4(1)：25–43.
[28] MODIRIASARI A，BOBET A，PYRAK-NOLTE L J. Active seismic monitoring of crack initiation，propagation，and coalescence in rock[J]. Rock Mechanics and Rock Engineering，2017，50(9)：2 311–2 325.
[29] WU J Y，NGUYEN V P，NGUYEN C T，et al. Phase-field modeling of fracture[J]. Advances in Applied Mechanics，2020，53：1–183.
[30] 杨庆，刘元俊. 岩石类材料裂纹扩展贯通的颗粒流模拟[J]. 岩石力学与工程学报，2012，31(增1)：3 123–3 129.(YANG Qing，LIU Yuanjun. Simulations of crack propagation in rock-link materials using particle flow code[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(Supp.1)：3 123–3 129.(in Chinese))
[31] 李鹏飞，朱其志，顾水涛，等. 岩石类材料裂隙形成和扩展的相场方法模拟[J]. 工程力学，2018，35(3)：41–48.(LI Pengfei，ZHU Qizhi，GU Shuitao，et al. A phase field method to simulate crack nucleation and crack propagation in rock-like materials[J]. Engineering Mechanics，2018，35(3)：41–48.(in Chinese))