Incorporation of tension-compression asymmetry into plastic damage phase-field modeling of quasi brittle geomaterials

Alessi, 2014, Gradient damage models coupled with plasticity and nucleation of cohesive cracks, Arch. Ration. Mech. Anal., 214, 575, 10.1007/s00205-014-0763-8 Alessi, 2015, Gradient damage models coupled with plasticity: variational formulation and main properties, Mech. Mater., 80, 351, 10.1016/j.mechmat.2013.12.005 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 Ambati, 2016, A phase-field model for ductile fracture at finite strains and its experimental verification, Comput. Mech., 57, 149, 10.1007/s00466-015-1225-3 Ambrosio, 1990, Approximation of functional depending on jumps by elliptic functional via α-convergence, Commun. 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 Barenblatt, 1962, The mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech., 7, 55, 10.1016/S0065-2156(08)70121-2 Barlat, 2003, Plane stress yield function for aluminum alloy sheets. part 1: theory, Int. J. Plast., 19, 1297, 10.1016/S0749-6419(02)00019-0 Barras, 2017, Interplay between process zone and material heterogeneities for dynamic cracks, Phys. Rev. Lett., 119, 10.1103/PhysRevLett.119.144101 Bažant, 1986, Shear fracture tests of concrete, Mater. Struct., 19, 111, 10.1007/BF02481755 Bažant, 2002, Nonlocal integral formulations of plasticity and damage: survey of progress, J. Eng. Mech., 128, 1119, 10.1061/(ASCE)0733-9399(2002)128:11(1119) Bažant, 1988, Nonlocal continuum damage, localization instability and convergence, J. Appl. Mech., 55, 287, 10.1115/1.3173674 Bažant, 1989, Measurement of characteristic length of nonlocal continuum, J. Eng. Mech., 115, 755, 10.1061/(ASCE)0733-9399(1989)115:4(755) Bažant, 1997, vol. 16 Belytschko, 2010, Coarse-graining of multiscale crack propagation, Int. J. Numer. Methods Eng., 81, 537, 10.1002/nme.2694 Bleyer, 2018, Phase-field modeling of anisotropic brittle fracture including several damage mechanisms, Comput. Methods Appl. Mech. Eng., 336, 213, 10.1016/j.cma.2018.03.012 Bobet, 1998, Fracture coalescence in rock-type materials under uniaxial and biaxial compression, Int. J. Rock Mech. Min. Sci., 35, 863, 10.1016/S0148-9062(98)00005-9 Borden, 2012 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. Eng., 312, 130, 10.1016/j.cma.2016.09.005 Borden, 2012, A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Eng., 217, 77, 10.1016/j.cma.2012.01.008 Bourdin, 2000, Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, 48, 797, 10.1016/S0022-5096(99)00028-9 Braides, 1998 Brandt, 1977, Multi-level adaptive solutions to boundary-value problems, Math. Comput., 31, 333, 10.1090/S0025-5718-1977-0431719-X Broumand, 2013, The extended finite element method for large deformation ductile fracture problems with a non-local damage-plasticity model, Eng. Fract. Mech., 112–113, 97, 10.1016/j.engfracmech.2013.10.002 Bryant, 2018, A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics, Comput. Methods Appl. Mech. Eng., 342, 561, 10.1016/j.cma.2018.08.008 Cazes, 2009, A thermodynamic method for the construction of a cohesive law from a nonlocal damage model, Int. J. Solids Struct., 46, 1476, 10.1016/j.ijsolstr.2008.11.019 Cen, 2017, Direct shear tests of sandstone under constant normal tensile stress condition using a simple auxiliary device, Rock Mech. Rock Eng., 50, 1425, 10.1007/s00603-017-1179-1 Cervera, 2017, An energy-equivalent d+/d- damage model with enhanced microcrack closure-reopening capabilities for cohesive-frictional materials, Materials, 10, 433, 10.3390/ma10040433 Chandra, 2002, Some issues in the application of cohesive zone models for metal-ceramic interfaces, Int. J. Solids Struct., 39, 2827, 10.1016/S0020-7683(02)00149-X Chen, 2017, Instability in dynamic fracture and the failure of the classical theory of cracks, Nat. Phys., 13, 1186, 10.1038/nphys4237 Chiarelli, 2003, Modeling of elastoplastic damage behavior of a claystone, Int. J. Plast., 19, 23, 10.1016/S0749-6419(01)00017-1 Cho, 2008, Development of a shear zone in brittle rock subjected to direct shear, Int. J. Rock Mech. Min. Sci., 45, 1335, 10.1016/j.ijrmms.2008.01.019 Choo, 2018, Coupled phase-field and plasticity modeling of geological materials: from brittle fracture to ductile flow, Comput. Methods Appl. Mech. Eng., 330, 1, 10.1016/j.cma.2017.10.009 Cicekli, 2007, A plasticity and anisotropic damage model for plain concrete, Int. J. Plast., 23, 1874, 10.1016/j.ijplas.2007.03.006 Collins, 1997, Application of thermomechanical principles to the modelling of geotechnical materials, Proc. Roy. Soc. A, 453, 1975, 10.1098/rspa.1997.0107 Comi, 2001, A non-local model with tension and compression damage mechanisms, Eur. J. Mech. A Solid., 20, 1, 10.1016/S0997-7538(00)01111-6 Comi, 2001, Fracture energy based bi-dissipative damage model for concrete, Int. J. Solids Struct., 38, 6427, 10.1016/S0020-7683(01)00066-X Crété, 2014, Numerical modelling of crack propagation in ductile materials combining the gtn model and x-fem, Comput. Methods Appl. Mech. Eng., 275, 204, 10.1016/j.cma.2014.03.007 Dafalias, 2003, A simple model for describing yield surface evolution during plastic flow, 169 Dai, 2018, Removal of singularities in hoek-brown criterion and its numerical implementation and applications, Int. J. Geomech., 18, 10.1061/(ASCE)GM.1943-5622.0001201 de Borst, 2012 de Borst, 2004, Discrete vs smeared crack models for concrete fracture: bridging the gap, Int. J. Numer. Anal. Methods Geomech., 28, 583, 10.1002/nag.374 de Borst, 2016, Gradient damage vs phase-field approaches for fracture: similarities and differences, Comput. Methods Appl. Mech. Eng., 312, 78, 10.1016/j.cma.2016.05.015 de Souza Neto, 2011 De Suvranu, 2017, A phase-field model for shock-induced α-γ phase transition of rdx, Int. J. Plast., 88, 140, 10.1016/j.ijplas.2016.10.006 Deng, 2010, Coarse-graining atomistic dynamics of brittle fracture by finite element method, Int. J. Plast., 26, 1402, 10.1016/j.ijplas.2010.04.007 Duda, 2015, A phase-field/gradient damage model for brittle fracture in elastic-plastic solids, Int. J. Plast., 65, 269, 10.1016/j.ijplas.2014.09.005 Dugdale, 1960, Yielding of steel sheets containing slits, J. Mech. Phys. Solids, 8, 100, 10.1016/0022-5096(60)90013-2 Ehlers, 2017, A phase-field approach embedded in the theory of porous media for the description of dynamic hydraulic fracturing, Comput. Methods Appl. Mech. Eng., 315, 348, 10.1016/j.cma.2016.10.045 Engelen, 2003, Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour, Int. J. Plast., 19, 403, 10.1016/S0749-6419(01)00042-0 Feenstra, 1996, A composite plasticity model for concrete, Int. J. Solids Struct., 33, 707, 10.1016/0020-7683(95)00060-N Feigenbaum, 2007, Directional distortional hardening in metal plasticity within thermodynamics, Int. J. Solids Struct., 44, 7526, 10.1016/j.ijsolstr.2007.04.025 Gao, 1999, Mechanism-based strain gradient plasticity-i. theory, J. Mech. Phys. Solids, 47, 1239, 10.1016/S0022-5096(98)00103-3 Gültekin, 2018, Numerical aspects of anisotropic failure in soft biological tissues favor energy-based criteria: a rate-dependent anisotropic crack phase-field model, Comput. Methods Appl. Mech. Eng., 331, 23, 10.1016/j.cma.2017.11.008 Gurson, 1977, Continuum theory of ductile rupture by void nucleation and growth: Part i-yield criteria and flow rules for porous ductile media, J. Eng. Mater. Technol., 99, 2, 10.1115/1.3443401 Hashiguchi, 2001, On the thermomechanical approach to the formulation of plastic constitutive equations, Soils Found., 41, 89, 10.3208/sandf.41.4_89 Hillerborg, 1976, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement Concr. Res., 6, 773, 10.1016/0008-8846(76)90007-7 Hoek, 2014, Fracture initiation and propagation in intact rock–a review, J. Rock Mech. Geotech. Eng., 6, 287, 10.1016/j.jrmge.2014.06.001 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 Horii, 1986, Brittle failure in compression: splitting faulting and brittle-ductile transition, Philos. Trans. Roy. Soc. A, 319, 337, 10.1098/rsta.1986.0101 Houlsby, 2000, A thermomechanical framework for constitutive models for rate-independent dissipative materials, Int. J. Plast., 16, 1017, 10.1016/S0749-6419(99)00073-X Huespe, 2009, A finite thickness band method for ductile fracture analysis, Int. J. Plast., 25, 2349, 10.1016/j.ijplas.2009.03.005 Hutchinson, 1983, Fundamentals of the phenomenological theory of nonlinear fracture mechanics, J. Appl. Mech., 50, 1042, 10.1115/1.3167187 Kachanov, 2013, vol. 10 Karsan, 1969, Behavior of concrete under compressive loadings, J. Struct. Div., 95, 2543, 10.1061/JSDEAG.0002424 Kuhn, 2010, A continuum phase field model for fracture, Eng. Fract. Mech., 77, 3625, 10.1016/j.engfracmech.2010.08.009 Kupfer, 1969, Behavior of concrete under biaxial stresses, J. Eng. Mech. Div., 99, 853 Lajtai, 1969, Strength of discontinuous rocks in direct shear, Geotechnique, 19, 218, 10.1680/geot.1969.19.2.218 Larsen, 2010, Existence of solutions to a regularized model of dynamic fracture, Math. Model. Methods Appl. Sci., 20, 1021, 10.1142/S0218202510004520 Lee, 2011, Modeling the viscoplastic micromechanical response of two-phase materials using fast fourier transforms, Int. J. Plast., 27, 707, 10.1016/j.ijplas.2010.09.002 Lemaitre, 1985, A continuous damage mechanics model for ductile fracture, J. Eng. Mater. Technol., 107, 83, 10.1115/1.3225775 Levitas, 2018, Thermodynamically consistent and scale-dependent phase field approach for crack propagation allowing for surface stresses, Int. J. Plast., 111, 1, 10.1016/j.ijplas.2018.07.005 Li, 2003, Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models, Int. J. Plast., 19, 849, 10.1016/S0749-6419(02)00008-6 Lorentz, 1999, A variational formulation for nonlocal damage models, Int. J. Plast., 15, 119, 10.1016/S0749-6419(98)00057-6 Lubliner, 1989, A plastic-damage model for concrete, Int. J. Solids Struct., 25, 299, 10.1016/0020-7683(89)90050-4 Ma, 2016, Failure characteristics of two porous sandstones subjected to true triaxial stresses, J. Geophys. Res. C Ocean. Atmos.: Solid Earth, 121, 6477 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. Eng., 199, 2765, 10.1016/j.cma.2010.04.011 Miehe, 2015, Phase field modeling of fracture in multi-physics problems. part i. balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids, Comput. Methods Appl. Mech. Eng., 294, 449, 10.1016/j.cma.2014.11.016 Miehe, 2010, Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations, Int. J. Numer. Methods Eng., 83, 1273, 10.1002/nme.2861 Moës, 1999, A finite element method for crack growth without remeshing, Int. J. Numer. Methods Eng., 46, 131, 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J Mozaffari, 2016, Coupled gradient damage–viscoplasticty model for ductile materials: phase field approach, Int. J. Plast., 83, 55, 10.1016/j.ijplas.2016.04.003 Murakami, 2012, vol. 185 Nestler, 2011, Phase-field modeling of multi-component systems, Curr. Opin. Solid State Mater. Sci., 15, 93, 10.1016/j.cossms.2011.01.003 Nguyen, 2017, Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials, Comput. Mech., 60, 289, 10.1007/s00466-017-1409-0 Nuismer, 1975, An energy release rate criterion for mixed mode fracture, Int. J. Fract., 11, 245, 10.1007/BF00038891 Palmer, 1973, The growth of slip surfaces in the progressive failure of over-consolidated clay, Proc. Roy. Soc. A, 332, 527, 10.1098/rspa.1973.0040 Park, 2009, Crack coalescence in specimens with open and closed flaws: a comparison, Int. J. Rock Mech. Min. Sci., 46, 819, 10.1016/j.ijrmms.2009.02.006 Park, 2008 Perdikaris, 1995, Size effect on fracture energy of concrete and stability issues in three-point bending fracture toughness testing, Mater. J., 92, 483 Ramsey, 2004, Hybrid fracture and the transition from extension fracture to shear fracture, Nature, 428, 63, 10.1038/nature02333 Rao, 2003, Shear fracture (mode ii) of brittle rock, Int. J. Rock Mech. Min. Sci., 40, 355, 10.1016/S1365-1609(03)00003-0 Remmers, 2003, A cohesive segments method for the simulation of crack growth, Comput. Mech., 31, 69, 10.1007/s00466-002-0394-z Revil-Baudard, 2018, Effect of the yield stresses in uniaxial tension and pure shear on the size of the plastic zone near a crack, Int. J. Plast., 102, 101, 10.1016/j.ijplas.2017.12.006 Roe, 2003, An irreversible cohesive zone model for interface fatigue crack growth simulation, Eng. Fract. Mech., 70, 209, 10.1016/S0013-7944(02)00034-6 Rosakis, 2000, A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals, J. Mech. Phys. Solids, 48, 581, 10.1016/S0022-5096(99)00048-4 Schlüter, 2014, Phase field approximation of dynamic brittle fracture, Comput. Mech., 54, 1141, 10.1007/s00466-014-1045-x Schneider, 2016, Phase-field modeling of crack propagation in multiphase systems, Comput. Methods Appl. Mech. Eng., 312, 186, 10.1016/j.cma.2016.04.009 Shen, 1994, Modification of the g-criterion for crack propagation subjected to compression, Eng. Fract. Mech., 47, 177, 10.1016/0013-7944(94)90219-4 Shen, 1995, Coalescence of fractures under shear stresses in experiments, J. Geophys. Res. Solid Ear., 100, 5975, 10.1029/95JB00040 Shi, 2015, A generalized thermodynamically consistent distortional hardening model for mg alloys, Int. J. Plast., 74, 158, 10.1016/j.ijplas.2015.06.010 Silling, 2000, Reformulation of elasticity theory for discontinuities and long-range forces, J. Mech. Phys. Solids, 48, 175, 10.1016/S0022-5096(99)00029-0 Silling, 2005, A meshfree method based on the peridynamic model of solid mechanics, Comput. Struct., 83, 1526, 10.1016/j.compstruc.2004.11.026 Svedberg, 1997, A thermodynamically consistent theory of gradient-regularized plasticity coupled to damage, Int. J. Plast., 13, 669, 10.1016/S0749-6419(97)00033-8 Tadmor, 1996, Quasicontinuum analysis of defects in solids, Philos. Mag. A, 73, 1529, 10.1080/01418619608243000 Trädegård, 1998, Fem-remeshing technique applied to crack growth problems, Comput. Methods Appl. Mech. Eng., 160, 115, 10.1016/S0045-7825(97)00287-9 Tvergaard, 1984, Analysis of the cup-cone fracture in a round tensile bar, Acta Metall., 32, 157, 10.1016/0001-6160(84)90213-X Wecharatana, 1983, Predictions of nonlinear fracture process zone in concrete, J. Eng. Mech., 109, 1231, 10.1061/(ASCE)0733-9399(1983)109:5(1231) Wilson, 2016, Phase-field modeling of hydraulic fracture, J. Mech. Phys. Solids, 96, 264, 10.1016/j.jmps.2016.07.019 Wu, 2017, A unified phase-field theory for the mechanics of damage and quasi-brittle failure, J. Mech. Phys. Solids, 103, 72, 10.1016/j.jmps.2017.03.015 Xiong, 2011, Coarse-grained atomistic simulation of dislocations, J. Mech. Phys. Solids, 59, 160, 10.1016/j.jmps.2010.11.005 Xu, 2013, An elastic–plastic cohesive zone model for metal–ceramic interfaces at finite deformations, Int. J. Plast., 41, 147, 10.1016/j.ijplas.2012.09.008 Xu, 2016, Mesh refinement schemes for the concurrent atomistic-continuum method, Int. J. Solids Struct., 90, 144, 10.1016/j.ijsolstr.2016.03.030 Yang, 2018, Energy dissipation analysis of elastic–plastic materials, Comput. Methods Appl. Mech. Eng., 331, 309, 10.1016/j.cma.2017.11.009 Yang, 2013, Concurrent atomistic and continuum simulation of strontium titanate, Acta Mater., 61, 89, 10.1016/j.actamat.2012.09.032 Zhang, 2001 Zhang, 2017, A modification of the phase-field model for mixed mode crack propagation in rock-like materials, Comput. Methods Appl. Mech. Eng., 322, 123, 10.1016/j.cma.2017.04.028 Zhang, 2017, Numerical evaluation of the phase-field model for brittle fracture with emphasis on the length scale, Comput. Mech., 59, 737, 10.1007/s00466-017-1373-8 Zhao, 2018, A micro-mechanics based plastic damage model for quasi-brittle materials under a large range of compressive stress, Int. J. Plast., 100, 156, 10.1016/j.ijplas.2017.10.004 Zhou, 2004, Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency, Int. J. Numer. Methods Eng., 59, 2000, 10.1002/nme.857 Zhu, 2017, A new rock strength criterion from microcracking mechanisms which provides theoretical evidence of hybrid failure, Rock Mech. Rock Eng., 50, 341, 10.1007/s00603-016-1083-0 Zhu, 2017, Peridynamic formulations enriched with bond rotation effects, Int. J. Eng. Sci., 121, 118, 10.1016/j.ijengsci.2017.09.004 Zhu, 2015, A refined micromechanical damage–friction model with strength prediction for rock-like materials under compression, Int. J. Solids Struct., 60–61, 75, 10.1016/j.ijsolstr.2015.02.005 Zhu, 2017, Micromechanics of rock damage: advances in the quasi-brittle field, J. Rock Mech. Geotech. Eng., 9, 29, 10.1016/j.jrmge.2016.11.003 Zhu, 2010, A micromechanics-based elastoplastic damage model for granular materials at low confining pressure, Int. J. Plast., 26, 586, 10.1016/j.ijplas.2009.09.006 Zhu, 2016, Analytical and numerical analysis of frictional damage in quasi brittle materials, J. Mech. Phys. Solids, 92, 137, 10.1016/j.jmps.2016.04.002 Ziegler, 1987, The derivation of constitutive relations from the free energy and the dissipation function, vol. 25, 183