A new hybrid phase-field model for modeling mixed-mode cracking process in anisotropic plastic rock-like materials

Aliha, 2012, Typical upper bound–lower bound mixed mode fracture resistance envelopes for rock material, Rock Mech. Rock Eng., 45, 65, 10.1007/s00603-011-0167-0 Ambati, 2015, Phase-field modeling of ductile fracture, Comput. Mech., 55, 1017, 10.1007/s00466-015-1151-4 Ambati, 2015, A review on phase-field models of brittle fracture and a new fast hybrid formulation, Comput. Mech., 55, 383, 10.1007/s00466-014-1109-y Ambrosio, 1990, Approximation of functional depending on jumps by elliptic functional via t-convergence, Comm. Pure Appl. Math., 43, 999, 10.1002/cpa.3160430805 Amor, 2009, Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments, J. Mech. Phys. Solids, 57, 1209, 10.1016/j.jmps.2009.04.011 Arriaga, 2017, Combined stability analysis of phase-field dynamic fracture and shear band localization, Int. J. Plast., 96, 81, 10.1016/j.ijplas.2017.04.018 ASTM, 2001, 6671-01, Standard test method for mixed mode I-Mode II interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites, 03 Benzeggagh, 1996, Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus, Compos. Sci. Technol., 56, 439, 10.1016/0266-3538(96)00005-X Bleyer, 2018, Phase-field modeling of anisotropic brittle fracture including several damage mechanisms, Comput. Methods Appl. Mech. Engrg., 336, 213, 10.1016/j.cma.2018.03.012 Bourdin, 2000, Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, 48, 797, 10.1016/S0022-5096(99)00028-9 Bryant, 2018, A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics, Comput. Methods Appl. Mech. Engrg., 342, 561, 10.1016/j.cma.2018.08.008 Bui, 2011, A modified benzeggagh-kenane fracture criterion for mixed-mode delamination, J. Compos. Mater., 45, 389, 10.1177/0021998310376105 Cao, 2020, A novel FFT-based phase field model for damage and cracking behavior of heterogeneous materials, Int. J. Plast., 133, 10.1016/j.ijplas.2020.102786 Cao, 2020, Numerical homogenization of elastic properties and plastic yield stress of rock-like materials with voids and inclusions at same scale, Eur. J. Mech. A Solids, 81, 103958, 10.1016/j.euromechsol.2020.103958 Chen, 2017, Fracture evolution characteristics of sandstone containing double fissures and a single circular hole under uniaxial compression, Int. J. Mining Sci. Technol., 27, 499, 10.1016/j.ijmst.2017.03.027 Chong, 1988, New specimens for mixed mode fracture investigations of geomaterials, Eng. Fract. Mech., 30, 701, 10.1016/0013-7944(88)90160-9 Choo, 2018, Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow, Comput. Methods Appl. Mech. Engrg., 330, 1, 10.1016/j.cma.2017.10.009 Dittmann, 2018, Variational phase-field formulation of non-linear ductile fracture, Comput. Methods Appl. Mech. Engrg., 342, 71, 10.1016/j.cma.2018.07.029 Fang, 2019, Phase field fracture in elasto-plastic solids: Abaqus implementation and case studies, Theor. Appl. Fract. Mech., 103, 10.1016/j.tafmec.2019.102252 Fei, 2021, Double-phase-field formulation for mixed-mode fracture in rocks, Comput. Methods Appl. Mech. Engrg., 376, 10.1016/j.cma.2020.113655 Feigenbaum, 2007, Directional distortional hardening in metal plasticity within thermodynamics, Int. J. Solids Struct., 44, 7526, 10.1016/j.ijsolstr.2007.04.025 Francfort, 1998, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46, 1319, 10.1016/S0022-5096(98)00034-9 Griffith, 1921, Vi. The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 221, 163 Hofacker, 2012, Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation, Int. J. Fract., 178, 113, 10.1007/s10704-012-9753-8 Hoffman, 1967, The brittle strength of orthotropic materials, J. Compos. Mater., 1, 200, 10.1177/002199836700100210 Ingraffea, 1980, Finite element models for rock fracture mechanics, Int. J. Numer. Anal. Methods Geomech., 4, 25, 10.1002/nag.1610040103 Lajtai, 1974, Brittle fracture in compression, Int. J. Fract., 10, 525, 10.1007/BF00155255 Lee, 2021, A model for irreversible deformation phenomena driven by hydrostatic stress, deviatoric stress and an externally applied field, Internat. J. Engrg. Sci., 169, 10.1016/j.ijengsci.2021.103573 Lee, 2021, Plasticity and enzymatic degradation coupled with volumetric growth in pulmonary hypertension progression, J. Biomech. Eng., 143, 10.1115/1.4051383 Lee, 2019, Morphological aspects of crack growth in rock materials with various flaws, Int. J. Numer. Anal. Methods Geomech., 43, 1854, 10.1002/nag.2938 Li, 2015, Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy, Internat. J. Numer. Methods Engrg., 102, 711, 10.1002/nme.4726 Li, 2013, Evaluating the applicability of fracture criteria to predict the crack evolution path of dolomite based on SCB experiments and FEM, Math. Probl. Eng., 2013, 10.1155/2013/959806 Li, 2021, Anisotropic elastoplastic phase field fracture modeling of 3D printed materials, Comput. Methods Appl. Mech. Engrg., 386, 10.1016/j.cma.2021.114086 Liu, 2021 Liu, 2015, Effects of deviatoric stress and structural anisotropy on compressive creep behavior of a clayey rock, Appl. Clay Sci., 114, 491, 10.1016/j.clay.2015.06.039 Mandal, 2021, Fracture of thermo-elastic solids: Phase-field modeling and new results with an efficient monolithic solver, Comput. Methods Appl. Mech. Engrg., 376, 10.1016/j.cma.2020.113648 Meng, 2020, Mesoscale computational modeling of concrete-like particle-reinforced composites with non-convex aggregates, Comput. Struct., 240, 106349, 10.1016/j.compstruc.2020.106349 Miehe, 2016, Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory, Int. J. Plast., 84, 1, 10.1016/j.ijplas.2016.04.011 Miehe, 2010, A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Comput. Methods Appl. Mech. Engrg., 199, 2765, 10.1016/j.cma.2010.04.011 Miehe, 2010, Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, Internat. J. Numer. Methods Engrg., 83, 1273, 10.1002/nme.2861 Nguyen, 2017, Phase field modelling of anisotropic crack propagation, Eur. J. Mech. A Solids, 65, 279, 10.1016/j.euromechsol.2017.05.002 Park, 2020, A new approach for fracture prediction considering general anisotropy of metal sheets, Int. J. Plast., 124, 199, 10.1016/j.ijplas.2019.08.011 Peng, 2021, New ductile fracture model for fracture prediction ranging from negative to high stress triaxiality, Int. J. Plast., 145, 10.1016/j.ijplas.2021.103057 Ramsey, 2004, Hybrid fracture and the transition from extension fracture to shear fracture, Nature, 428, 63, 10.1038/nature02333 Rubin, 2015, A unified theoretical structure for modeling interstitial growth and muscle activation in soft tissues, Internat. J. Engrg. Sci., 90, 1, 10.1016/j.ijengsci.2014.12.005 Shen, 2022, Approximate plastic yield criteria of geomaterials with pores and grains embedded in a porous matrix, Int. J. Plast., 153, 103275, 10.1016/j.ijplas.2022.103275 Shen, 2011, Macroscopic yield criterion for ductile materials containing randomly oriented spheroidal cavities, Int. J. Damage Mech., 20, 1198, 10.1177/1056789510395552 Shen, 2017, Approximate macroscopic yield criteria for Drucker-Prager type solids with spheroidal voids, Int. J. Plast., 99, 221, 10.1016/j.ijplas.2017.09.008 Simoes, 2021, Phase field modelling of fracture and fatigue in Shape Memory Alloys, Comput. Methods Appl. Mech. Engrg., 373, 10.1016/j.cma.2020.113504 Tao, 2021, Phase-field modeling of 3D fracture in elasto-plastic solids based on the modified GTN theory, Eng. Fract. Mech. Teichtmeister, 2017, Phase field modeling of fracture in anisotropic brittle solids, Int. J. Non-Linear Mech., 97, 1, 10.1016/j.ijnonlinmec.2017.06.018 Ulloa, 2022, A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior, J. Mech. Phys. Solids, 159, 10.1016/j.jmps.2021.104684 Wang, 2018, Mechanical and crack evolution characteristics of coal–rock under different fracture-hole conditions: a numerical study based on particle flow code, Environ. Earth Sci., 77, 1, 10.1007/s12665-018-7486-3 Wang, 2022, Numerical study of time-dependent deformation and cracking in brittle rocks with phase-field method and application to slope instability analysis, Int. J. Rock Mech. Min. Sci., 155, 10.1016/j.ijrmms.2022.105144 Wu, 2018, A length scale insensitive phase-field damage model for brittle fracture, J. Mech. Phys. Solids, 119, 20, 10.1016/j.jmps.2018.06.006 Wu, 2020, Chapiter one - phase field modeling of fracture, Adv. Appl. Mech., 53, 1, 10.1016/bs.aams.2019.08.001 Yang, 2011, Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression, Int. J. Fract., 168, 227, 10.1007/s10704-010-9576-4 Yang, 2018, Energy dissipation analysis of elastic–plastic materials, Comput. Methods Appl. Mech. Engrg., 331, 309, 10.1016/j.cma.2017.11.009 Yang, 2020, Plastic-energy dissipation in pressure-dependent materials, J. Eng. Mech., 146, 10.1061/(ASCE)EM.1943-7889.0001728 Yin, 2018, Investigation on mechanical behavior and crack coalescence of sandstone specimens containing fissure-hole combined flaws under uniaxial compression., Geosci. J., 22, 10.1007/s12303-017-0081-x You, 2020, Incorporation of tension-compression asymmetry into plastic damage phase-field modeling of quasi brittle geomaterials, Int. J. Plast., 124, 71, 10.1016/j.ijplas.2019.08.003 Yu, 2021, Numerical modeling of deformation and damage around underground excavation by phase-field method with hydromechanical coupling, Comput. Geotech., 138, 10.1016/j.compgeo.2021.104369 Yu, 2021, Numerical study of thermo-hydro-mechanical responses of in situ heating test with phase-field model, Int. J. Rock Mech. Min. Sci., 138, 10.1016/j.ijrmms.2020.104542 Zhang, 2018 Zhang, 2017, A modification of the phase-field model for mixed mode crack propagation in rock-like materials, Comput. Methods Appl. Mech. Engrg., 322, 123, 10.1016/j.cma.2017.04.028 Zhou, 2019, Phase-field modeling of fluid-driven dynamic cracking in porous media, Comput. Methods Appl. Mech. Engrg., 350, 169, 10.1016/j.cma.2019.03.001 Zhu, 2019