Meta-modeling game for deriving theory-consistent, microstructure-based traction–separation laws via deep reinforcement learning

Kun Wang1, WaiChing Sun1
1Department of Civil Engineering and Engineering Mechanics, Columbia University, 614 SW Mudd, Mail Code: 4709, New York, NY 10027, United States

Tài liệu tham khảo

Rice, 1968, A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 35, 379, 10.1115/1.3601206 Park, 2009, A unified potential-based cohesive model of mixed-mode fracture, J. Mech. Phys. Solids, 57, 891, 10.1016/j.jmps.2008.10.003 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 Bryant, 2018, A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics, Comput. Methods Appl. Mech. Engrg., 10.1016/j.cma.2018.08.008 Rabczuk, 2006, A new approach for modelling slip lines in geological materials with cohesive models, Int. J. Numer. Anal. Methods Geomech., 30, 1159, 10.1002/nag.522 Borja, 2007, Continuum mathematical modeling of slip weakening in geological systems, J. Geophys. Res. Solid Earth, 112, 10.1029/2005JB004056 Elices, 2002, The cohesive zone model: advantages, limitations and challenges, Eng. Fract. Mech., 69, 137, 10.1016/S0013-7944(01)00083-2 Ohnaka, 1989, A cohesive zone model for dynamic shear faulting based on experimentally inferred constitutive relation and strong motion source parameters, J. Geophys. Res. Solid Earth, 94, 4089, 10.1029/JB094iB04p04089 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 Sun, 2018, Prediction of permeability and formation factor of sandstone with hybrid lattice Boltzmann/finite element simulation on microtomographic images, Int. J. Rock Mech. Mining Sci., 106, 269, 10.1016/j.ijrmms.2018.04.020 Ortiz, 1999, Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, Internat. J. Numer. Methods Engrg., 44, 1267, 10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7 Rudnicki, 1980, Fracture mechanics applied to the Earth’s crust, Ann. Rev. Earth Planet. Sci., 8, 489, 10.1146/annurev.ea.08.050180.002421 Paterson, 2005 Sun, 2013, A unified method to predict diffuse and localized instabilities in sands, Geomech. Geoeng., 8, 65, 10.1080/17486025.2012.695403 Borja, 2013 Wang, 2016, Identifying material parameters for a micro-polar plasticity model via x-ray micro-ct images: lessons learned from the curve-fitting exercises, Int. J. Multiscale Comput. Eng., 14, 389, 10.1615/IntJMultCompEng.2016016841 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 Moës, 2003, A computational approach to handle complex microstructure geometries, Comput. Methods Appl. Mech. Engrg., 192, 3163, 10.1016/S0045-7825(03)00346-3 Hirschberger, 2008, Computational homogenization of material layers with micromorphic mesostructure, Phil. Mag., 88, 3603, 10.1080/14786430802502567 Hirschberger, 2009, Computational multiscale modelling of heterogeneous material layers, Eng. Fract. Mech., 76, 793, 10.1016/j.engfracmech.2008.10.018 Feyel, 2003, A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua, Comput. Methods Appl. Mech. Engrg., 192, 3233, 10.1016/S0045-7825(03)00348-7 Sun, 2011, Connecting microstructural attributes and permeability from 3D tomographic images of in situ shear-enhanced compaction bands using multiscale computations, Geophys. Res. Lett., 38, 10.1029/2011GL047683 Sun, 2011, Multiscale method for characterization of porous microstructures and their impact on macroscopic effective permeability, Internat. J. Numer. Methods Engrg., 88, 1260, 10.1002/nme.3220 Fish, 2013 Sun, 2013, A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band, Acta Geotech., 8, 465, 10.1007/s11440-013-0210-2 Wang, 2015, Anisotropy of a tensorial Bishop’s coefficient for wetted granular materials, J. Eng. Mech., 143, B4015004, 10.1061/(ASCE)EM.1943-7889.0001005 Liu, 2016, A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials, Internat. J. Numer. Methods Engrg., 106, 129, 10.1002/nme.5139 Kuhn, 2015, Stress-induced anisotropy in granular materials: fabric, stiffness, and permeability, Acta Geotech., 10, 399, 10.1007/s11440-015-0397-5 Wang, 2016, A semi-implicit discrete-continuum coupling method for porous media based on the effective stress principle at finite strain, Comput. Methods Appl. Mech. Engrg., 304, 546, 10.1016/j.cma.2016.02.020 Wu, 2018, Multiscale modeling and analysis of compaction bands in high-porosity sandstones, Acta Geotech., 13, 575, 10.1007/s11440-017-0560-2 Kirane, 2008, A cold dwell fatigue crack nucleation criterion for polycrystalline Ti-6242 using grain-level crystal plasticity FE model, Int. J. Fatigue, 30, 2127, 10.1016/j.ijfatigue.2008.05.026 Verhoosel, 2010, Computational homogenization for adhesive and cohesive failure in quasi-brittle solids, Internat. J. Numer. Methods Engrg., 83, 1155, 10.1002/nme.2854 Keshavarz, 2013, Multi-scale crystal plasticity finite element model approach to modeling nickel-based superalloys, Acta Mater., 61, 6549, 10.1016/j.actamat.2013.07.038 Panchal, 2013, Key computational modeling issues in integrated computational materials engineering, Comput. Aided Des., 45, 4, 10.1016/j.cad.2012.06.006 Faisal, 2014, Computational study of the elastic properties of Rheum rhabarbarum tissues via surrogate models of tissue geometry, J. Struct. Biol., 185, 285, 10.1016/j.jsb.2014.01.012 Liu, 2016, Determining material parameters for critical state plasticity models based on multilevel extended digital database, J. Appl. Mech., 83, 011003, 10.1115/1.4031619 Tallman, 2017, Reconciled top-down and bottom-up hierarchical multiscale calibration of bcc fe crystal plasticity, Int. J. Multiscale Comput. Eng., 15, 10.1615/IntJMultCompEng.2017021859 Le, 2015, Computational homogenization of nonlinear elastic materials using neural networks, Internat. J. Numer. Methods Engrg., 104, 1061, 10.1002/nme.4953 Bessa, 2017, A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality, Comput. Methods Appl. Mech. Engrg., 320, 633, 10.1016/j.cma.2017.03.037 Versino, 2017, Data driven modeling of plastic deformation, Comput. Methods Appl. Mech. Engrg., 318, 981, 10.1016/j.cma.2017.02.016 Kafka, 2018, Data-driven mechanistic modeling of influence of microstructure on high-cycle fatigue life of nickel titanium, JOM, 1 Wulfinghoff, 2018, Model order reduction of nonlinear homogenization problems using a Hashin–Shtrikman type finite element method, Comput. Methods Appl. Mech. Engrg., 330, 149, 10.1016/j.cma.2017.10.019 Lefik, 2002, Artificial neural network for parameter identifications for an elasto-plastic model of superconducting cable under cyclic loading, Comput. Struct., 80, 1699, 10.1016/S0045-7949(02)00162-1 Pan, 2010, A survey on transfer learning, IEEE Trans. Knowl. Data Eng., 22, 1345, 10.1109/TKDE.2009.191 Sutton, 1992, Introduction: The challenge of reinforcement learning, 1 Silver, 2016, Mastering the game of Go with deep neural networks and tree search, nature, 529, 484, 10.1038/nature16961 Silver, 2017, Mastering the game of Go without human knowledge, Nature, 550, 354, 10.1038/nature24270 Shannon, 1950, XXII. programming a computer for playing chess, London Edinburgh Dublin Phil. Mag. J. Sci., 41, 256, 10.1080/14786445008521796 Bellman, 1957, A Markovian decision process, J. Math. Mech., 679 Dolcetta, 1984, Approximate solutions of the Bellman equation of deterministic control theory, Appl. Math. Optim., 11, 161, 10.1007/BF01442176 Sun, 2013, A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain, Int. J. Numer. Anal. Methods Geomech., 37, 2755, 10.1002/nag.2161 Sun, 2014, Modeling the hydro-mechanical responses of strip and circular punch loadings on water-saturated collapsible geomaterials, Acta Geotech., 9, 903, 10.1007/s11440-013-0276-x Sun, 2015, A stabilized finite element formulation for monolithic thermo-hydro-mechanical simulations at finite strain, Internat. J. Numer. Methods Engrg., 103, 798, 10.1002/nme.4910 Salinger, 2016, Albany: using component-based design to develop a flexible, generic multiphysics analysis code, Int. J. Multiscale Comput. Eng., 14, 10.1615/IntJMultCompEng.2016017040 Bang-Jensen, 2008 Hagberg, 2008 Kendall, 1946, The advanced theory of statistics Anderson, 1954, A test of goodness of fit, J. Amer. Statist. Assoc., 49, 765, 10.1080/01621459.1954.10501232 Scholz, 1987, K-sample anderson–darling tests, J. Amer. Statist. Assoc., 82, 918 Hornik, 1989, Multilayer feedforward networks are universal approximators, Neural Netw., 2, 359, 10.1016/0893-6080(89)90020-8 Hochreiter, 1997, Long short-term memory, Neural Comput., 9, 1735, 10.1162/neco.1997.9.8.1735 Cho, 2014 Chollet, 2015 Pedregosa, 2011, Scikit-learn: machine learning in python, J. Mach. Learn. Res., 12, 2825 Kingma, 2014 Silver, 2017 Browne, 2012, A survey of monte carlo tree search methods, IEEE Tran. Comput. Intell. AI Games, 4, 1, 10.1109/TCIAIG.2012.2186810 Nasrabadi, 2007, Pattern recognition and machine learning, J. Electron. Imaging, 16, 049901, 10.1117/1.2819119 Mnih, 2015, Human-level control through deep reinforcement learning, Nature, 518, 529, 10.1038/nature14236 Battaglia, 2018 Fu, 2011, Fabric evolution within shear bands of granular materials and its relation to critical state theory, Int. J. Numer. Anal. Methods Geomech., 35, 1918, 10.1002/nag.988 Li, 2011, Anisotropic critical state theory: role of fabric, J. Eng. Mech., 138, 263, 10.1061/(ASCE)EM.1943-7889.0000324 Pastor, 2011, Computational geomechanics: the heritage of Olek Zienkiewicz, Internat. J. Numer. Methods Engrg., 87, 457, 10.1002/nme.3192 Timoshenko, 1953 Mehrabadi, 1982, On statistical description of stress and fabric in granular materials, Int. J. Numer. Anal. Methods Geomech., 6, 95, 10.1002/nag.1610060107 Dafalias, 2004, Simple plasticity sand model accounting for fabric change effects, J. Eng. Mech., 130, 622, 10.1061/(ASCE)0733-9399(2004)130:6(622) Dafalias, 2004, Sand plasticity model accounting for inherent fabric anisotropy, J. Eng. Mech., 130, 1319, 10.1061/(ASCE)0733-9399(2004)130:11(1319) Tordesillas, 2011, Discovering community structures and dynamical networks from grain-scale kinematics of shear bands in sand, 67 Tordesillas, 2010, Force cycles and force chains, Phys. Rev. E, 81, 011302, 10.1103/PhysRevE.81.011302 Williams, 1997, Coherent vortex structures in deforming granular materials, Mech. Cohesive-frictional Mater. Int. J. Exp. Model. Comput. Mater. Struct., 2, 223 Liu, 2018, Coupled flow network and discrete element modeling of injection-induced crack propagation and coalescence in brittle rock, Acta Geotech., 1 Oliver, 2002, From continuum mechanics to fracture mechanics: the strong discontinuity approach, Eng. Fract. Mech., 69, 113, 10.1016/S0013-7944(01)00060-1 Šmilauer, 2010, Yade reference documentation, Yade Documentation, 474 Cundall, 1979, A discrete numerical model for granular assemblies, Geotechnique, 29, 47, 10.1680/geot.1979.29.1.47