Phase field modeling of frictional slip with slip weakening/strengthening under non-isothermal conditions

Eric C. Bryant1, WaiChing Sun1
1Department of Civil Engineering and Engineering Mechanics, Columbia University, 614 SW Mudd, Mail Code: 4709, New York, NY 10027, United States of America

Tài liệu tham khảo

Segall, 1983, Nucleation and growth of strike slip faults in granite., J. Geophys. Res., 88, 555, 10.1029/JB088iB01p00555 Lavier, 2000, Factors controlling normal fault offset in an ideal brittle layer, J. Geophys. Res. Solid Earth, 105, 23431, 10.1029/2000JB900108 Bai, 2002, Orthogonal cross joints: Do they imply a regional stress rotation?, J. Struct. Geol., 24, 77, 10.1016/S0191-8141(01)00050-5 Choi, 2013, Using core complex geometry to constrain fault strength, Geophys. Res. Lett., 40, 3863, 10.1002/grl.50732 Wang, 1994, Wear processes during frictional sliding of rock: a theoretical and experimental study, J. Geophys. Res., 99, 6789, 10.1029/93JB02875 Menéndez, 1996, Micromechanics of brittle faulting and cataclastic flow in berea sandstone, J. Struct. Geol., 18, 1, 10.1016/0191-8141(95)00076-P Paterson, 2005 Wang, 2018, A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning, Comput. Methods Appl. Mech. Engrg., 334, 337, 10.1016/j.cma.2018.01.036 Wang, 2019, Meta-modeling game for deriving theory-consistent, microstructure-based traction–separation laws via deep reinforcement learning, Comput. Methods Appl. Mech. Engrg., 346, 216, 10.1016/j.cma.2018.11.026 Rudnicki, 1980, Fracture mechanics applied to the earth’s crust., Ann. Rev. Earth Planetary sciences: volume 8, 8, 489, 10.1146/annurev.ea.08.050180.002421 Pollard, 1987, Theoretical displacements and stresses near fractures in rock: With applications to faults, joints, veins, dikes, and solution surfaces, 277 Aochi, 2000, Selectivity of spontaneous rupture propagation on a branched fault, Geophys. Res. Lett., 27, 3635, 10.1029/2000GL011560 Fliss, 2005, Fault branching and rupture directivity, J. Geophys. Res. Solid Earth, 110, 1 Ortiz, 1987, A finite element method for localized failure analysis, Comput. Methods Appl. Mech. Engrg., 61, 189, 10.1016/0045-7825(87)90004-1 Simo, 1993, A new class of algorithms for classical plasticity extended to finite strains. Application to geomaterials, Comput. Mech., 11, 253, 10.1007/BF00371865 Regueiro, 2001, Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity, Int. J. Solids Struct., 38, 3647, 10.1016/S0020-7683(00)00250-X Linder, 2007, Finite elements with embedded strong discontinuities for the modeling of failure in solids, Internat. J. Numer. Methods Engrg., 72, 1391, 10.1002/nme.2042 Borja, 2008, Assumed enhanced strain and the extended finite element methods: A unification of concepts, Comput. Methods Appl. Mech. Engrg., 197, 2789, 10.1016/j.cma.2008.01.019 Wang, 2018, A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning, Comput. Methods Appl. Mech. Engrg., 334, 337, 10.1016/j.cma.2018.01.036 Wang, 2019, An updated Lagrangian LBM–DEM–FEM coupling model for dual-permeability fissured porous media with embedded discontinuities, Comput. Methods Appl. Mech. Engrg., 344, 276, 10.1016/j.cma.2018.09.034 Moës, 1999, A finite element method for crack growth without remeshing, Internat. J. Numer. Methods Engrg., 46, 131, 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J Prevost, 2016, Faults simulations for three-dimensional reservoir-geomechanical models with the extended finite element method, J. Mech. Phys. Solids, 86, 1, 10.1016/j.jmps.2015.09.014 Liu, 2019, Modeling branched and intersecting faults in reservoir-geomechanics models with the extended finite element method, Int. J. Numer. Anal. Methods Geomech., 43, 2075, 10.1002/nag.2949 Sun, 2017, Mixed arlequin method for multiscale poromechanics problems, Internat. J. Numer. Methods Engrg., 111, 624, 10.1002/nme.5476 De Borst, 2003, Numerical aspects of cohesive-zone models, Eng. Fract. Mech., 70, 1743, 10.1016/S0013-7944(03)00122-X Park, 2011, Cohesive zone models: a critical review of traction-separation relationships across fracture surfaces, Appl. Mech. Rev., 64, 10.1115/1.4023110 Mota, 2008, Fracture and fragmentation of simplicial finite element meshes using graphs, Internat. J. Numer. Methods Engrg., 73, 1547, 10.1002/nme.2135 Mousavi, 2010, Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method, Comput. Methods Appl. Mech. Engrg., 199, 3237, 10.1016/j.cma.2010.06.031 Chevaugeon, 2013, Improved crack tip enrichment functions and integration for crack modeling using the extended finite element method, Int. J. Multiscale Comput. Eng., 11, 10.1615/IntJMultCompEng.2013006523 Linder, 2009, Finite elements with embedded branching, Finite Elem. Anal. Des., 45, 280, 10.1016/j.finel.2008.10.012 Stazi, 2003, An extended finite element method with higher-order elements for curved cracks, Comput. Mech., 31, 38, 10.1007/s00466-002-0391-2 Fournier, 2012, Insights to slip behavior on rough faults using discrete element modeling, Geophys. Res. Lett., 39, 10.1029/2012GL051899 Tomac, 2017, Coupled hydro-thermo-mechanical modeling of hydraulic fracturing in quasi-brittle rocks using BPM-dem, J. Rock Mech. Geotech. Eng., 9, 92, 10.1016/j.jrmge.2016.10.001 Xu, 2020, Discrete element modeling of transversely isotropic rocks with non-continuous planar fabrics under Brazilian test, Acta Geotech., 1 Aydin, 2006, Geological and mathematical framework for failure modes in granular rock, J. Struct. Geol., 28, 83, 10.1016/j.jsg.2005.07.008 Bourdin, 2008, The variational approach to fracture, Var. Approach Fract., 91, 1 Borden, 2012, A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Engrg., 217–220, 77, 10.1016/j.cma.2012.01.008 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 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 Geelen, 2019, A phase-field formulation for dynamic cohesive fracture, Comput. Methods Appl. Mech. Engrg., 348, 680, 10.1016/j.cma.2019.01.026 Suh, 2019, An open-source fenics implementation of a phase field fracture model for micropolar continua, Int. J. Multiscale Comput. Eng., 17, 10.1615/IntJMultCompEng.2020033422 Suh, 2020, A phase field model for cohesive fracture in micropolar continua, Comput. Methods Appl. Mech. Engrg., 369, 10.1016/j.cma.2020.113181 Ambrosio, 2013, A variational model for plastic slip and its regularization viaγ-convergence, J. Elasticity, 110, 201, 10.1007/s10659-012-9390-5 Alessi, 2018, Comparison of phase-field models of fracture coupled with plasticity, 1 Fei, 2020, A phase-field method for modeling cracks with frictional contact, Internat. J. Numer. Methods Engrg., 121, 740, 10.1002/nme.6242 Ambrosio, 2013, A variational model for plastic slip and its regularization via Γ-convergence, J. Elasticity, 110, 201, 10.1007/s10659-012-9390-5 Ruina, 1983, Slip instability and state variable friction laws., J. Geophys. Res., 88, 10359, 10.1029/JB088iB12p10359 Dieterich, 1986, A model for the nucleation of earthquake slip, 37 Chester, 1994, Effects of temperature on friction: constitutive equations and experiments with quartz gouge, J. Geophys. Res., 99, 7247, 10.1029/93JB03110 Borja, 2007, Continuum mathematical modeling of slip weakening in geological systems, J. Geophys. Res. Solid Earth, 112, 549 Foster, 2007, Embedded strong discontinuity finite elements for fractured geomaterials with variable friction, Internat. J. Numer. Methods Engrg., 72, 549, 10.1002/nme.2020 Liu, 2009, An extended finite element framework for slow-rate frictional faulting with bulk plasticity and variable friction, Int. J. Numer. Anal. Methods Geomech., 33, 1535, 10.1002/nag.777 Ziaei-Rad, 2016, Identifying the crack path for the phase field approach to fracture with non-maximum suppression, Comput. Methods Appl. Mech. Engrg., 312, 304, 10.1016/j.cma.2016.08.025 Hu, 2020, A phase-field model of fracture with frictionless contact and random fracture properties: Application to thin-film fracture and soil desiccation, Comput. Methods Appl. Mech. Engrg., 368, 10.1016/j.cma.2020.113106 Forest, 2009, Micromorphic approach for gradient elasticity, viscoplasticity, and damage, J. Eng. Mech., 135, 117, 10.1061/(ASCE)0733-9399(2009)135:3(117) Forest, 2016, Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage, Proc. R. Soc. A, 472, 10.1098/rspa.2015.0755 Miehe, 2016, Phase-field modelling of ductile fracture: A variational gradient-extended plasticity-damage theory and its micromorphic regularization, Phil. Trans. R. Soc. A, 374, 10.1098/rsta.2015.0170 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, 2011, A multi-field incremental variational framework for gradient-extended standard dissipative solids, J. Mech. Phys. Solids, 59, 898, 10.1016/j.jmps.2010.11.001 Aldakheel, 2017, Micromorphic approach for gradient-extended thermo-elastic–plastic solids in the logarithmic strain space, Contin. Mech. Thermodyn., 29, 1207, 10.1007/s00161-017-0571-0 Eringen, 1968, Mechanics of micromorphic continua, 18 Ambrosio, 1990, Approximation of functional depending on jumps by elliptic functional via t-convergence, Comm. Pure Appl. Math., 43, 999, 10.1002/cpa.3160430805 Wilson, 2013, A phase-field model for fracture in piezoelectric ceramics, Int. J. Fract., 183, 135, 10.1007/s10704-013-9881-9 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 Simo, 1992, Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation, Comput. Methods Appl. Mech. Engrg., 98, 41, 10.1016/0045-7825(92)90170-O Abbo, 1995, A smooth hyperbolic approximation to the mohr-Coulomb yield criterion, Comput. Struct., 54, 427, 10.1016/0045-7949(94)00339-5 Young, 2009, Liquefaction potential of coastal slopes induced by solitary waves, Acta Geotech., 4, 17, 10.1007/s11440-009-0083-6 Na, 2019, A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables, Comput. Methods Appl. Mech. Engrg., 357, 10.1016/j.cma.2019.112572 Bryant, 2019, A micromorphically regularized cam-clay model for capturing size-dependent anisotropy of geomaterials, Comput. Methods Appl. Mech. Engrg., 354, 56, 10.1016/j.cma.2019.05.003 Chester, 1992, Multimechanism friction constitutive model for ultrafine quartz gouge at hypocentral conditions, J. Geophys. Res., 97, 1859, 10.1029/91JB02349 Ben-Zion, 1995, Slip patterns and earthquake populations along different classes of faults in elastic solids, J. Geophys. Res., 100 Lapusta, 2000, Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate- and state-dependent friction, J. Geophys. Res. Solid Earth, 105, 23765, 10.1029/2000JB900250 Rice, 2001, Rate and state dependent friction and the stability of sliding between elastically deformable solids, J. Mech. Phys. Solids, 49, 1865, 10.1016/S0022-5096(01)00042-4 Putelat, 2010, Regimes of frictional sliding of a spring-block system, J. Mech. Phys. Solids, 58, 27, 10.1016/j.jmps.2009.09.001 Putelat, 2011, On the microphysical foundations of rate-and-state friction, J. Mech. Phys. Solids, 59, 1062, 10.1016/j.jmps.2011.02.002 Borja, 2013, 255 Stesky, 1978, Mechanisms of high temperature frictional sliding in westerly granite., Can J. Earth Sci., 15, 361, 10.1139/e78-042 Scholz, 1972, Static fatigue of quartz, J. Geophys. Res., 77, 2104, 10.1029/JB077i011p02104 Liu, 2020, Shift boundary material point method: an image-to-simulation workflow for solids of complex geometries undergoing large deformation, Comput. Particle Mech., 7, 291, 10.1007/s40571-019-00239-y Liu, 2020, Ils-mpm: an implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles, Comput. Methods Appl. Mech. Eng., 369, 113168, 10.1016/j.cma.2020.113168 Wang, 2020, A non-cooperative meta-modeling game for automated third-party calibrating, validating, and falsifying constitutive laws with parallelized adversarial attacks, Comput. Methods Appl. Mech. Eng. Gurtin, 1996, Generalized ginzburg-landau and cahn-hilliard equations based on a microforce balance, Physica D, 92, 178, 10.1016/0167-2789(95)00173-5 Borden, 2016, A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects, Comput. Methods Appl. Mech. Engrg., 312, 130, 10.1016/j.cma.2016.09.005 Na, 2018, Computational thermomechanics of crystalline rock, part i: A combined multi-phase-field/crystal plasticity approach for single crystal simulations, Comput. Methods Appl. Mech. Engrg., 338, 657, 10.1016/j.cma.2017.12.022 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 McAuliffe, 2015, A unified model for metal failure capturing shear banding and fracture, Int. J. Plast., 65, 131, 10.1016/j.ijplas.2014.08.016 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 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 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, 2015, Phase field modeling of fracture in multi-physics problems. Part II. coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids, Comput. Methods Appl. Mech. Engrg., 294, 486, 10.1016/j.cma.2014.11.017 Wang, 2017, A unified variational eigen-erosion framework for interacting brittle fractures and compaction bands in fluid-infiltrating porous media, Comput. Methods Appl. Mech. Engrg., 318, 1, 10.1016/j.cma.2017.01.017 Stein, 2020, A smoothness energy without boundary distortion for curved surfaces, ACM Trans. Graph., 39, 1, 10.1145/3377406 Calakli, 2011, Ssd: Smooth signed distance surface reconstruction, Comput. Graph. Forum, 30, 1993, 10.1111/j.1467-8659.2011.02058.x Lopez, 1999, Evaluation of methods for ridge and valley detection, IEEE Trans. Pattern Anal. Mach. Intell., 21, 327, 10.1109/34.761263 Cornelis, 2013, Crack detection and inpainting for virtual restoration of paintings: The case of the ghent altarpiece, Signal Process., 93, 605, 10.1016/j.sigpro.2012.07.022 López, 2000, Multilocal creaseness based on the level-set extrinsic curvature, Comput. Vis. Image Underst., 77, 111, 10.1006/cviu.1999.0812 Armero, 1992, A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems, Internat. J. Numer. Methods Engrg., 35, 737, 10.1002/nme.1620350408 Armero, 1993, A priori stability estimates and unconditionally stable product formula algorithms for nonlinear coupled thermoplasticity, Int. J. Plast., 9, 749, 10.1016/0749-6419(93)90036-P Bangerth, 2007, Deal.ii - -a general-purpose object-oriented finite element library, ACM Trans. Math. Software, 33, 24, 10.1145/1268776.1268779 White, 2008, Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients, Comput. Methods Appl. Mech. Engrg., 197, 4353, 10.1016/j.cma.2008.05.015 Choo, 2016, Hydromechanical modeling of unsaturated flow in double porosity media, Int. J. Geomech., 16, 10.1061/(ASCE)GM.1943-5622.0000558 Na, 2017, Computational thermo-hydro-mechanics for multiphase freezing and thawing porous media in the finite deformation range, Comput. Methods Appl. Mech. Engrg., 318, 667, 10.1016/j.cma.2017.01.028 Choo, 2018, Cracking and damage from crystallization in pores: Coupled chemo-hydro-mechanics and phase-field modeling, Comput. Methods Appl. Mech. Engrg., 335, 347, 10.1016/j.cma.2018.01.044 Borja, 2001, Strain localization in frictional materials exhibiting displacement jumps, Comput. Methods Appl. Mech. Engrg., 190, 2555, 10.1016/S0045-7825(00)00253-X Horai, 1971, Thermal conductivity of rock-forming minerals, J. Geophys. Res., 76, 1278, 10.1029/JB076i005p01278 Cho, 2009, The thermal conductivity for granite with various water contents, Eng. Geol., 107, 167, 10.1016/j.enggeo.2009.05.012 Liu, 2008, A contact algorithm for frictional crack propagation with the extended finite element method, Internat. J. Numer. Methods Engrg., 76, 1489, 10.1002/nme.2376 Sanz, 2007, Mechanical aspects of thrust faulting driven by far-field compression and their implications for fold geometry, Acta Geotech., 2, 17, 10.1007/s11440-007-0025-0 Reyes, 1991, Failure mechanisms of fractured rock - a fracture coalescence model, 333 Bobet, 1998, Numerical modeling of fracture coalescence in a model rock material, Int. J. Fract., 92, 221, 10.1023/A:1007460316400 Dolbow, 2001, An extended finite element method for modeling crack growth with frictional contact, Comput. Methods Appl. Mech. Engrg., 190, 6825, 10.1016/S0045-7825(01)00260-2 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 Kunin, 1981, An algebra of tensor operators and its applications to elasticity, Internat. J. Engrg. Sci., 19, 1551, 10.1016/0020-7225(81)90078-1 Walpole, 1984, Fourth-rank tensors of the thirty-two crystal classes: multiplication tables, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 391, 149 Itskov, 2000, On the theory of fourth-order tensors and their applications in computational mechanics, Comput. Methods Appl. Mech. Engrg., 189, 419, 10.1016/S0045-7825(99)00472-7 Dutko, 1993, Universal anisotropic yield criterion based on superquadric functional representation: Part 1. Algorithmic issues and accuracy analysis, Comput. Methods Appl. Mech. Engrg., 109, 73, 10.1016/0045-7825(93)90225-M Cuitino, 1992, A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics, Eng. Comput., 9, 437, 10.1108/eb023876 De Borst, 1994, A note on the calculation of consistent tangent operators for von mises and Drucker-Prager plasticity, Commun. Numer. Methods. Eng., 10, 1021, 10.1002/cnm.1640101208 De Souza Neto, 2008, 1 Pandolfi, 2012, An eigenerosion approach to brittle fracture, Internat. J. Numer. Methods Engrg., 92, 694, 10.1002/nme.4352