Multi Field Simulation of Fracture

Advani, 1997, Consequences of fluid lag in three-dimensional hydraulic fracture, International Journal for Numerical and Analytical Methods in Geomechanics, 21, 229, 10.1002/(SICI)1096-9853(199704)21:4<229::AID-NAG862>3.0.CO;2-V Ainsworth, 1997, A posteriori error estimation in finite element analysis, Computer Methods in Applied Mechanics and Engineering, 142, 1, 10.1016/S0045-7825(96)01107-3 Akbari, 2010, Analysis of thermoelastic waves in a two-dimensional functionally graded materials domain by the meshless local Petrov-Galerkin method, Computer Modeling in Engineering and Sciences, 65, 27 Alber, 2012, Second order asymptotics for the propagation speed of interfaces in the Allen-Cahn phase field model for elastic solids, Proceedings in Applied Mathematics and Mechanics, 12, 31, 10.1002/pamm.201210009 Al-Busaidi, 2005, Distinct element modeling of hydraulically fractured Lac du Bonnet granite, Journal of Geophysical Research, 110, 10.1029/2004JB003297 Amiri, 2014, XLME interpolants, a seamless bridge between XFEM and enriched meshless methods, Computational Mechanics, 53, 45, 10.1007/s00466-013-0891-2 Amiri, 2014, Phase-field modeling of fracture in linear thin shells, Theoretical and Applied Fracture Mechanics, 69, 102, 10.1016/j.tafmec.2013.12.002 Babuška, 1997, The partition of unity method, International Journal for Numerical Methods in Engineering, 40, 727, 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N Bae, 2001, Subinterfacial cracks in bimaterial systems subjected to mechanical and thermal loading, Engineering Fracture Mechanics, 68, 1081, 10.1016/S0013-7944(01)00005-4 Bangert, 2004, Chemo-hygro-mechanical modelling and numerical simulation of concrete deterioration caused by alkali–silica reaction, International Journal for Numerical and Analytical Methods in Geomechanics, 28, 689, 10.1002/nag.375 Barbieri, 2013, Multiple crack growth and coalescence in meshfree methods with a distance function-based enriched kernel, Key Engineering Materials, 560, 37, 10.4028/www.scientific.net/KEM.560.37 Barbieri, 2012, A new weight-function enrichment in meshless methods for multiple cracks in linear elasticity, International Journal for Numerical Methods in Engineering, 90, 177, 10.1002/nme.3313 Barenblatt, 1959, The formation of equilibrium cracks during brittle fracture: General ideas and hypotheses. Axially-symmetric cracks, Journal of Applied Mathematics and Mechanics, 23, 622, 10.1016/0021-8928(59)90157-1 Barros, 2004, On error estimator and p-adaptivity in the generalized finite element method, International Journal for Numerical Methods in Engineering, 60, 2373, 10.1002/nme.1048 Bastien Masse, 2010 Bathe, 1996 Bažant, 1996, Analysis of work-of-fracture method for measuring fracture energy of concrete, Journal of Engineering Mechanics, 122, 138, 10.1061/(ASCE)0733-9399(1996)122:2(138) Bažant, 2002, Concrete fracture models: Testing and practice, Engineering Fracture Mechanics, 69, 165, 10.1016/S0013-7944(01)00084-4 Behnia, 2011, On the crack propagation modeling of hydraulic fracturing by a hybridized displacement discontinuity/boundary collocation method, Journal of Mining and Environment, 2, 1 Bernard, 2012, Damage growth modeling using the thick level set (TLS) approach: Efficient discretization for quasi-static loadings, Computer Methods in Applied Mechanics and Engineering, 233–236, 11, 10.1016/j.cma.2012.02.020 Biot, 1957, The elastic coefficients of the theory of consolidation, Journal of Applied Mechanics, 24, 594, 10.1115/1.4011606 Bolzon, 2001, Finite elements with embedded displacement discontinuity: A generalized variable formulation, Computational Mechanics, 27, 463, 10.1007/s004660100257 Bolzon, 1997, A discrete formulation for elastic solids with damaging interfaces, Computer Methods in Applied Mechanics and Engineering, 140, 329, 10.1016/S0045-7825(96)01101-2 Bolzon, 2000, Finite elements with embedded displacement discontinuity: A generalized variable formulation, International Journal for Numerical Methods in Engineering, 49, 1227, 10.1002/1097-0207(20001210)49:10<1227::AID-NME2>3.0.CO;2-Z Boone, 1990, A numerical procedure for simulation of hydraulically driven fracture propagation in poroelastic media, International Journal for Numerical and Analytical Methods in Geomechanics, 14, 27, 10.1002/nag.1610140103 Bordas, 2007, Derivative recovery and a posteriori error estimate for extended finite elements, Computer Methods in Applied Mechanics and Engineering, 196, 3381, 10.1016/j.cma.2007.03.011 Bordas, 2008, A simple error estimator for extended finite elements, Communications in Numerical Methods in Engineering, 24, 961, 10.1002/cnm.1001 Bordas, 2006, Enriched finite elements and level sets for damage tolerance assessment of complex structures, Engineering Fracture Mechanics, 73, 1176, 10.1016/j.engfracmech.2006.01.006 Bordas, 2011, On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM), International Journal for Numerical Methods in Engineering, 86, 637, 10.1002/nme.3156 Bordas, 2007, An extended finite element library, International Journal for Numerical Methods in Engineering, 71, 703, 10.1002/nme.1966 Bordas, 2010, Strain smoothing in FEM and XFEM, Computers & Structures, 88, 1419, 10.1016/j.compstruc.2008.07.006 Bordas, 2010, Alleviating the mesh burden Bordas, 2008, Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment, Engineering Fracture Mechanics, 75, 943, 10.1016/j.engfracmech.2007.05.010 Borden, 2012, A phase-field description of dynamic brittle fracture, Computer Methods in Applied Mechanics and Engineering, 217–220, 77, 10.1016/j.cma.2012.01.008 Boroomand, 1999, Recovery procedures in error estimation and adaptivity. Part II: Adaptivity in nonlinear problems of elasto-plasticity behavior, Computer Methods in Applied Mechanics and Engineering, 176, 127, 10.1016/S0045-7825(98)00333-8 Bourdin, 2008, The variational approach to fracture, Journal of Elasticity, 91, 5, 10.1007/s10659-007-9107-3 Bowyer, 1981, Computing Dirchelet tessellations, The Computer Journal, 24, 162, 10.1093/comjnl/24.2.162 Camacho, 1996, Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures, 33, 2899, 10.1016/0020-7683(95)00255-3 Camanho, 2003, Numerical simulation of mixed-mode progressive delamination in composite materials, Journal of Composite Materials, 37, 1415, 10.1177/0021998303034505 Carpinteri, 1989, Numerical analysis of catastrophic softening behavior (snap-back instability), Computer & Structures, 31, 607, 10.1016/0045-7949(89)90337-4 Carrier, 2012, Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model, Engineering Fracture Mechanics, 79, 312, 10.1016/j.engfracmech.2011.11.012 Carter, 2000, Simulating fully 3-D hydraulic fracturing, 525 Cast3M (2003): FE code developed by the French Atomic Agency (CEA), France. www-cast3m.cea.fr. Castonguay, 2013 Cervera, 2006, Mesh objective tensile cracking via a local continuum damage model and a crack tracking technique, Computer Methods in Applied Mechanics and Engineering, 196, 304, 10.1016/j.cma.2006.04.008 Chen, 2012, Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth, Computer Methods in Applied Mechanics and Engineering, 209, 250, 10.1016/j.cma.2011.08.013 Chen, 2001, A stabilized conforming nodal integration for Galerkin mesh-free methods, International Journal for Numerical Methods in Engineering, 50, 435, 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A Cleary, 1978, Moving singularities in elasto-diffusive solids with applications to fracture propagation, International Journal of Solids and Structures, 14, 81, 10.1016/0020-7683(78)90045-8 ConCrack de Borst, 2004, Discrete vs smeared crack models for concrete fracture: Bridging the gap, International Journal for Numerical and Analytical Methods in Geomechanics, 28, 583, 10.1002/nag.374 De Sa, 2012, Modeling of concrete nonlinear mechanical behavior at high temperatures with different damage-based approaches, Materials and Structures, 44, 1411, 10.1617/s11527-011-9707-z De Sa, 2008, Analysis of microcracking induced by differential drying shrinkage, Cement and Concrete Composites, 30, 947, 10.1016/j.cemconcomp.2008.06.015 De Schutter, 1997, Fracture energy of concrete at early ages, Materials and Structures, 30, 67, 10.1007/BF02486306 Detournay, 1991, Plane strain analysis of a stationary hydraulic fracture in aporoelastic medium, International Journal of Solids and Structures, 27, 1645, 10.1016/0020-7683(91)90067-P Dias-da-Costa, 2013, An embedded formulationwith conforming finite elements to capture strong discontinuities, International Journal for Numerical Methods in Engineering, 93, 224, 10.1002/nme.4393 Do, 2013, Improved cohesive stress integration schemes for cohesive zone elements, Engineering Fracture Mechanics, 107, 14, 10.1016/j.engfracmech.2013.04.009 Duflot, 2006, A meshless method with enriched weight functions for three-dimensional crack propagation, International Journal for Numerical Methods in Engineering, 65, 1970, 10.1002/nme.1530 Duflot, 2008, The extended finite element method in thermoelastic fracture mechanics, International Journal for Numerical Methods in Engineering, 74, 827, 10.1002/nme.2197 Duflot, 2008, A posteriori error estimation for extended finite elements by an extended global recovery, International Journal for Numerical Methods in Engineering, 76, 1123, 10.1002/nme.2332 Duflot, 2002, A truly meshless Galerkin method based on a moving least squares quadrature, Communications in Numerical Methods in Engineering, 18, 441, 10.1002/cnm.503 Duflot, 2004, Fatigue crack growth analysis by an enriched meshless method, Journal of Computational and Applied Mathematics, 168, 155, 10.1016/j.cam.2003.04.006 Duflot, 2004, A meshless method with enriched weight functions for fatigue crack growth, International Journal for Numerical Methods in Engineering, 59, 1945, 10.1002/nme.948 Dugdale, 1960, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, 8, 100, 10.1016/0022-5096(60)90013-2 Dumstorff, 2007, Crack propagation criteria in the framework of X-FEM-based structural analyses, International Journal for Numerical and Analytical Methods in Geomechanics, 31, 239, 10.1002/nag.560 Dunant, 2011, An algorithm to compute damage from load in composites, Frontiers of Architecture and Civil Engineering in China, 5, 180, 10.1007/s11709-011-0107-9 Dunant, 2010, Micro-mechanical modelling of alkali-silica-reaction-induced degradation using the AMIE framework, Cement and Concrete Research, 40, 517, 10.1016/j.cemconres.2009.07.024 Dunant, 2012, Effects of aggregate size on alkali-silica-reaction induced expansion, Cement and Concrete Research, 42, 745, 10.1016/j.cemconres.2012.02.012 Dvorkin, 1990, Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and mesh distortions, International Journal for Numerical Methods in Engineering, 30, 541, 10.1002/nme.1620300311 Elices, 2002, The cohesive zone model: Advantages, limitations and challenges, Engineering Fracture Mechanics, 69, 137, 10.1016/S0013-7944(01)00083-2 Ellsworth, 2013, Injection induced earthquakes, Science, 341, 142, 10.1126/science.1225942 Eshiet, 2011, Investigation of geo mechanical responses of reservoirs induced by carbon dioxide storage, 1318 Falk, 2001, A critical evaluation of cohesive zone models of dynamic fracture, Journal de Physique IV, 11, 43 Francfort, 1998, Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, 46, 1319, 10.1016/S0022-5096(98)00034-9 Ganis, 2014, Modeling fluid injection in fractures with a reservoir simulator coupled to a boundary element method, Computational Geosciences, 10.1007/s10596-013-9396-5 Garagash, 2000, The tip region of a fluid-driven fracture in an elastic medium, Journal of Applied Mechanics, 67, 183, 10.1115/1.321162 Gawin, 1999, Numerical analysis of hygro-thermic behaviour and damage of concrete at high temperature, Mechanics of Cohesive-Frictional Materials, 4, 37, 10.1002/(SICI)1099-1484(199901)4:1<37::AID-CFM58>3.0.CO;2-S Gawin, 2003, Modelling of thermo-chemical and mechanical damage of concrete at high temperature, Computer Methods in Applied Mechanics and Engineering, 192, 1731, 10.1016/S0045-7825(03)00200-7 Gawin, 2006, Towards prediction of the thermal spalling risk through a multi-phase porous media model of concrete, Computer Methods in Applied Mechanics and Engineering, 195, 5707, 10.1016/j.cma.2005.10.021 Gawin, 2006, Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part I: Hydration and hygro-thermal phenomena, International Journal for Numerical Methods in Engineering, 67, 299, 10.1002/nme.1615 Gawin, 2006, Hygro-thermo-chemo-mechanical modellingof concrete at early ages and beyond. Part II: Shrinkage and creep of concrete, International Journal for Numerical Methods in Engineering, 67, 332, 10.1002/nme.1636 Geertsma, 1969, A rapid method of predicting with and extent of hydraulically induced fracture, Journal of Petroleum Technology, 21, 1571, 10.2118/2458-PA Gerasimov, 2012, An explicit residual-type error estimator for Q1-quadrilateral extended finite element method in two-dimensional linear elastic fracture mechanics, International Journal for Numerical Methods in Engineering, 90, 1118, 10.1002/nme.3363 Giannopoulos, 2007, A BEM analysis for thermomechanical closure of interfacial cracks incorporating friction and thermal resistance, Computer Methods in Applied Mechanics and Engineering, 196, 1018, 10.1016/j.cma.2006.08.013 Gomez, 2000, Cracking in PMMA containing U-shaped notches, Fatigue and Fracture of Engineering Materials and Structures, 23, 795, 10.1046/j.1460-2695.2000.00264.x González-Estrada, 2014, Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery, Computational Mechanics, 53, 957, 10.1007/s00466-013-0942-8 González-Estrada, 2012, On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods, Engineering Computations, 29, 814, 10.1108/02644401211271609 González-Estrada, 2012 Gracie, 2008, Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods, International Journal for Numerical Methods in Engineering, 74, 1645, 10.1002/nme.2217 Grätsch, 2005, A posteriori error estimation techniques in practical finite element analysis, Computers & Structures, 83, 235, 10.1016/j.compstruc.2004.08.011 Gravouil, 2002, Non-planar 3D crack growth by the extended finite element and level sets-part II: Level set update, International Journal for Numerical Methods in Engineering, 53, 2569, 10.1002/nme.430 Gray, 2014 Gray, 2013, Averaging theory for description of environmental problems: What have we learned, Advances in Water Resources, 51, 123, 10.1016/j.advwatres.2011.12.005 Griffith, 1921, The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society A, 221, 163 Guduru, 2001, Dynamic full field measurements of crack tip temperatures, Engineering Fracture Mechanics, 68, 1535, 10.1016/S0013-7944(01)00045-5 Hakim, 2009, Laws of crack motion and phase-field models of fracture, Journal of the Mechanics and Physics of Solids, 57, 342, 10.1016/j.jmps.2008.10.012 Hilleborg, 1976, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research, 6, 773, 10.1016/0008-8846(76)90007-7 Howarth, 2011, Natural gas: Should fracking stop?, Nature, 477, 271, 10.1038/477271a Huang, 1985, Hydraulic fracturing of a saturated porous medium—I: General theory, Theoretical and Applied Fracture Mechanics, 4, 201, 10.1016/0167-8442(85)90005-9 Huang, 1985, Hydraulic fracturing of a saturated porous medium—II: Special cases, Theoretical and Applied Fracture Mechanics, 4, 215, 10.1016/0167-8442(85)90006-0 ICOLD, 1999 Idelsohn, 2006, Fluid-structure interaction using the particle finite element method, Computer Methods in Applied Mechanics and Engineering, 195, 2100, 10.1016/j.cma.2005.02.026 Irzal, 2013, Isogeometric finite element analysis of poro elasticity, International Journal for Numerical and Analytical Methods in Geomechanics, 37, 1891, 10.1002/nag.2195 Irzal, 2014, An isogeometric analysis Bézier interface element for mechanical and poromechanical fracture problems, International Journal for Numerical Methods in Engineering, 97, 608, 10.1002/nme.4615 Jiang, 2013, An edge-based smoothed XFEM for fracture in composite materials, International Journal of Fracture, 179, 179, 10.1007/s10704-012-9786-z Kachanov, 1986 Karihaloo, 2006, Accurate determination of cohesive crack tip fields using XFEM and admissible stress recovery Kerr, 2012, Learning how to NOT make your own earthquakes, Science, 335, 1436, 10.1126/science.335.6075.1436 Khoei, 2010, Modeling of dynamic cohesive fracture propagation in porous saturated media, International Journal for Numerical and Analytical Methods in Geomechanics, 35, 1160, 10.1002/nag.955 Khoei, 2011, Modeling of dynamic cohesive fracture propagation in porous saturated media, International Journal for Numerical and Analytical Methods in Geomechanics, 35, 1160, 10.1002/nag.955 Khoei, 2012, Thermo-hydro-mechanical modelling of impermeable discontinuity in saturated porous media with X-FEM technique, Engineering Fracture Mechanics, 96, 701, 10.1016/j.engfracmech.2012.10.003 Kraaijeveld, 2011, Propagating cracks in saturated ionized porous media, Vol. 55, 425 Kraaijeveldt, 2013, 2-D mode one crack propagation in saturated ionized porous media using partition of unity finite elements, Journal of Applied Mechanics, 80 Kuhl, 2000, An anisotropic gradient damage model for quasi-brittle materials, Computer Methods in Applied Mechanics and Engineering, 183, 87, 10.1016/S0045-7825(99)00213-3 Kuhn, 2010, A continuum phase field model for fracture, Engineering Fracture Mechanics, 77, 3625, 10.1016/j.engfracmech.2010.08.009 Larive, 1998 Lee, 1994, Errors indicators and adaptive remeshing in large deformations finite element analysis, Finite Elements in Analysis and Design, 16, 99, 10.1016/0168-874X(94)90044-2 Lemaitre, 1990 Lewis, 1989, Finite element modelling of two phase heat and fluid flow in deforming porous media, Transport in Porous Media, 4, 319, 10.1007/BF00165778 Lewis, 1998 Li, 2012, Numerical simulation of 3d hydraulic fracturing based on an improved flow-stress-damage model and a parallel fem technique, Rock Mechanics and Rock Engineering, 45, 801 Li, 2002, Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition, International Journal of Solids and Structures, 39, 1213, 10.1016/S0020-7683(01)00188-3 Li, 1998, Implementation and adaptivity of a space-time finite element method for structural dynamics, Computer Methods in Applied Mechanics and Engineering, 156, 211, 10.1016/S0045-7825(97)00207-7 Lian, 2012, Recent developments in CAD/analysis integration, Computational Technology Reviews, 6, 1, 10.4203/ctr.6.1 Lian, 2013, Stress analysis without meshing: Isogeometric boundary-element method, Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics, 166, 88 Lin, 2012, Enriched goal-oriented error estimation applied to fracture mechanics problems solved by XFEM, Acta Mechanica Solida Sinica, 25, 393, 10.1016/S0894-9166(12)60035-4 Liu, 2010, A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of fracture problems, International Journal for Numerical Methods in Engineering, 83, 1466, 10.1002/nme.2868 Markert, 2013, A survey of selected coupled multifield problems in computational mechanics, Journal of Coupled Systems and Multiscale Dynamics, 1, 22, 10.1166/jcsmd.2013.1007 Markert, 2013, A phase-field approach to hydraulic fracturing Markert, 2010, Comparison of monolithic and splitting solutionschemes for dynamic porous media problem, International Journal for Numerical Methods in Engineering, 82, 1341 Matallah, 2010, A practical method to estimate crack openings in concrete structures, International Journal for Numerical and Analytical Methods in Geomechanics, 34, 1541 Mauroux, 2012, Study of cracking due to drying in coating mortars by digital image correlation, Cement and Concrete Research, 42, 1014, 10.1016/j.cemconres.2012.04.002 Mazars, 1986, A description of micro and macroscale damage of concrete structures, Engineering Fracture Mechanics, 25, 729, 10.1016/0013-7944(86)90036-6 Mediavilla, 2006, A robust and consistent remeshing-transfer operator for ductile fracture simulations, Computers and Structures, 83, 604, 10.1016/j.compstruc.2005.10.007 Miehe, 2010, A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Computer Methods in Applied Mechanics and Engineering, 199, 2765, 10.1016/j.cma.2010.04.011 Mikelic, 2014 Milanese, 2014 Moës, 2002, Extended finite element method for cohesive crack growth, Engineering Fracture Mechanics, 69, 813, 10.1016/S0013-7944(01)00128-X Moës, 1999, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, 46, 131, 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J Moës, 2002, Non-planar 3D crack growth by the extended finite element and level sets-Part I: Mechanical model, International Journal for Numerical Methods in Engineering, 53, 2549, 10.1002/nme.429 Moës, 2011, A level set based model for damage growth: The thick level set approach, International Journal for Numerical Methods in Engineering, 86, 358, 10.1002/nme.3069 Moës, 2014, Coupling local and non-local damage evolution with the thick level set model, Advanced Modeling and Simulation in Engineering Sciences, 10.1186/s40323-014-0016-2 Mohammadnejad, 2013, Hydromechanical modelling of cohesive crack propagation in multiphase porous media using extended finite element method, International Journal for Numerical and Analytical Methods in Geomechanics, 37, 1247, 10.1002/nag.2079 Mohammadnejad, 2013, An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model, Finite Elements in Analysis and Design, 73, 77, 10.1016/j.finel.2013.05.005 Moreau, 2014, Explicit dynamics with a non-local damage model using the Thick Level Set approach, International Journal for Numerical Methods in Engineering Muravin, 2006, Multiple crack weight for solution of multiple interacting cracks by meshless numerical methods, International Journal for Numerical Methods in Engineering, 67, 1146, 10.1002/nme.1661 Nguyen, 2013 Nguyen, 2008, Meshless methods: A review and computer implementation aspects, Mathematics and Computers in Simulation, 79, 763, 10.1016/j.matcom.2008.01.003 Nguyen-Van, 2008, A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures, Computer Modeling in Engineering and Sciences, 23, 209 Nguyen-Xuan, 2009, An edge-based smoothed finite element method for analysis of two-dimensional piezoelectric structures, Smart Materials and Structures, 18, 065015, 10.1088/0964-1726/18/6/065015 Oñate, 2011, Possibilities of the particle finite element method for fluid-soil-structure interaction problems, Journal of Computational Mechanics, 48, 307, 10.1007/s00466-011-0617-2 Oñate, 2004, The particle finite element method. An overview, International Journal of Computational Methods, 1, 267, 10.1142/S0219876204000204 Ortiz, 1999, Finite deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, International Journal for Numerical Methods in Engineering, 44, 1267, 10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7 Panetier, 2010, Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM, International Journal for Numerical Methods in Engineering, 81, 671, 10.1002/nme.2705 Pannachet, 2009, Error estimation and adaptivity for discontinuous failure, International Journal for Numerical Methods in Engineering, 78, 528, 10.1002/nme.2495 Peerlings, 2002, Localisation issues in local and nonlocal continuum approaches to fracture, European Journal of Mechanics-A/Solids, 21, 175, 10.1016/S0997-7538(02)01211-1 Perić, 1996, Transfer operators for evolving meshes in small strain elasto-plasticity, Computer Methods in Applied Mechanics and Engineering, 137, 331, 10.1016/S0045-7825(96)01070-5 Perkins, 1961, Widths of hydraulic fractures, SPE Journal, 222, 937 Pesavento, 2012, Modeling alkali-silica reaction in non-isothermal, partially saturated cement based materials, Computer Methods in Applied Mechanics and Engineering, 225–228, 95, 10.1016/j.cma.2012.02.019 Phung-Van, 2013, Static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators by the cell-based smoothed discrete shear gap method (CS-FEM-DSG3), Smart Materials and Structures, 22, 095026, 10.1088/0964-1726/22/9/095026 Pizzocolo, 2013, Mode I crack propagation in hydrogels is stepwise, Engineering Fracture Mechanics, 97, 72, 10.1016/j.engfracmech.2012.10.018 Planas, 1992, Measurement of the fracture energy using three-point bend tests: Part 2: Influence of bulk energy dissipation, Materials and Structures, 25, 305, 10.1007/BF02472671 Prange, 2012, Error estimation for crack simulations using the XFEM, International Journal for Numerical Methods in Engineering, 91, 1459, 10.1002/nme.4331 Qiao, 2011, Augmented cohesive elements for efficient delamination analysis of composite laminates, Journal of Engineering Materials and Technology, 133, 0410101, 10.1115/1.4004694 Rabczuk, 2007, A meshfree thin shell method for non-linear dynamic fracture, International Journal for Numerical Methods in Engineering, 72, 524, 10.1002/nme.2013 Rabczuk, 2007, A simplified mesh-free method for shear bands with cohesive surfaces, International Journal for Numerical Methods in Engineering, 69, 993, 10.1002/nme.1797 Rabczuk, 2004, Cracking particles: A simplified meshfree method for arbitrary evolving cracks, International Journal for Numerical Methods in Engineering, 61, 2316, 10.1002/nme.1151 Rabczuk, 2010, On three-dimensional modelling of crack growth using partition of unity methods, Computers & Structures, 88, 1391, 10.1016/j.compstruc.2008.08.010 Rabczuk, 2008, A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures, Engineering Fracture Mechanics, 75, 4740, 10.1016/j.engfracmech.2008.06.019 Rabczuk, 2010, A simple and robust three-dimensional cracking-particle method without enrichment, Computer Methods in Applied Mechanics and Engineering, 199, 2437, 10.1016/j.cma.2010.03.031 Rank, 1983, On the importance of the discrete maximum principle in transient analysis using finite element methods, International Journal for Numerical Methods in Engineering, 19, 1771, 10.1002/nme.1620191205 Remmers, 2003, A cohesive segments method for the simulation of crack growth, Computational Mechanics, 31, 69, 10.1007/s00466-002-0394-z Réthoré, 2008, A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks, Computational Mechanics, 42, 227, 10.1007/s00466-007-0178-6 Rice, 1968, Mathematical analysis in the mechanics of fracture, Vol. 2, 191 Rice, 1976, Some basic stress diffusion solutions for fluid saturated elastic porous media with compressible constituents, Reviews of Geophsics and Space Physics, 14, 227, 10.1029/RG014i002p00227 Rice, 1969, Local heating by plastic deformation at crack tip Rizzato, 2014 Ródenas, 2010, Accurate recovery-based upper error bounds for the extended finite element framework, Computer Methods in Applied Mechanics and Engineering, 199, 2607, 10.1016/j.cma.2010.04.010 Ródenas, 2008, A recovery-type error estimator for the extended finite element method based on singular+ smooth stress field splitting, International Journal for Numerical Methods in Engineering, 76, 545, 10.1002/nme.2313 Rosa, 2012, A loading rate dependent cohesive model for concrete fracture, Engineering Fracture Mechanics, 82, 195, 10.1016/j.engfracmech.2011.12.013 Rots, 1988 Rüter, 2013, Goal-oriented explicit residual-type error estimates in XFEM, Computational Mechanics, 52, 361, 10.1007/s00466-012-0816-5 Rüter, 2011, Goal-oriented residual error estimates for XFEM approximations in LEFM, 231 Salerno, 2012, Avalanches in strained amorphous solids: Does inertia destroy critical behavior?, Physical Review Letters, 109, 105703, 10.1103/PhysRevLett.109.105703 Saucier, 1997, The challenge of numerical modeling of strains and stresses in concrete repairs, Cement and Concrete Research, 27, 1261, 10.1016/S0008-8846(97)00106-3 Schellekens, 1993, A nonlinear finite-element approach for the analysis of mode-I free edge delamination in composites, International Journal of Solids and Structures, 30, 1239, 10.1016/0020-7683(93)90014-X Schellekens, 1996, On the numerical modeling of edge delamination in composites, Key Engineering Materials, 121–122, 131, 10.4028/www.scientific.net/KEM.120-121.131 Schrefler, 2006, On adaptive refinement techniques in multifield problems including cohesive fracture, Computer Methods in Applied Mechanics and Engineering, 195, 444, 10.1016/j.cma.2004.10.014 Sciumè, 2013, A multiphysics model for concrete at early age applied to repairs problems, Engineering Structures, 57, 374, 10.1016/j.engstruct.2013.09.042 Sciumè, 2012, Thermo-hygro-chemo-mechanical modelling of the behaviour of a massive beam with restrained shrinkage Scott, 2013, Isogeometric boundary element analysis using unstructured T-splines, Computer Methods in Applied Mechanics and Engineering, 254, 197, 10.1016/j.cma.2012.11.001 Secchi, 2012, A method for 3-D hydraulic fracturing simulation, The International Journal of Fracture, 178, 245, 10.1007/s10704-012-9742-y Secchi, 2014, Hydraulic fracturing and its peculiarities, Asia Pacific Journal on Computational Engineering, 1, 8, 10.1186/2196-1166-1-8 Secchi, 2003, An improved procedure for 2-D unstructured Delaunay mesh generation, Advances in Engineering Software, 34, 217, 10.1016/S0965-9978(02)00131-X Secchi, 2004, Cohesive fracture growth in a thermoelastic bi-material medium, Computers and Structures, 82, 1875, 10.1016/j.compstruc.2004.03.059 Secchi, 2007, Mesh adaptation and transfer schemes for discrete fracture propagation in porous materials, International Journal for Numerical and Analytical Methods in Geomechanics, 31, 331, 10.1002/nag.581 Serebrinsky, 2004, A quantum-mechanically informed continuum model of hydrogen embrittlement, Journal of the Mechanics and Physics of Solids, 52, 2403, 10.1016/j.jmps.2004.02.010 Sethian, 1999 Shahrokhabadi, 2014, Modeling flow regime in shale using isogeometric analysis, 239 Simoni, 2003, Cohesive fracture mechanics for a multi-phase porous medium, Engineering with Computers, 20, 675, 10.1108/02644400310488817 Simoni, 2008, Numerical difficulties and computational procedures for thermo-hydro-mechanical coupled problems of saturated porous media, Computational Mechanics, 43, 179, 10.1007/s00466-008-0302-2 Simpson, 2013, An isogeometric boundary element method for elastostatic analysis: 2D implementation aspects, Computers & Structures, 118, 2, 10.1016/j.compstruc.2012.12.021 Simpson, 2012, A two-dimensional isogeometric boundary element method for elastostatic analysis, Computer Methods in Applied Mechanics and Engineering, 209, 87, 10.1016/j.cma.2011.08.008 Simpson, 2011, Evaluation of J1 and J2 integrals for curved cracks using an enriched boundary element method, Engineering Fracture Mechanics, 78, 623, 10.1016/j.engfracmech.2010.12.006 Simpson, 2011, A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics, Computer Methods in Applied Mechanics and Engineering, 200, 1, 10.1016/j.cma.2010.06.015 Sladek, 2008, Fracture analysis of cracks in magneto-electro-elastic solids by the MLPG, Computational Mechanics, 42, 697, 10.1007/s00466-008-0269-z Sladek, 2007, Fracture analyses in continuously nonhomogeneous piezoelectric solids by the MLPG, Computer Modeling in Engineering and Sciences, 19, 247 Spence, 1985, Self-similar solutions for elasto-hydrodynamic cavity flow, Proceedings of the Royal Society of London, 400, 289 Steffens, 2003, Ageing approach to water effect on alkali-silica reaction. Degradation of structures, Journal of Engineering Mechanics, 129, 50, 10.1061/(ASCE)0733-9399(2003)129:1(50) Stolz, 2012, A new model of damage: A moving thick layer approach, International Journal of Fracture, 174, 49, 10.1007/s10704-012-9693-3 Sukumar, 2008, Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method, International Journal for Numerical Methods in Engineering, 76, 727, 10.1002/nme.2344 Sukumar, 2001, Modeling holes and inclusions by level sets in the extended finite-element method, Computer Methods in Applied Mechanics and Engineering, 190, 6183, 10.1016/S0045-7825(01)00215-8 Turon, 2006, A damage model for the simulation of delamination in advanced composites under variable-mode loading, Mechanics of Materials, 38, 1072, 10.1016/j.mechmat.2005.10.003 Turska, 1993, On convergence conditions of partitioned solution procedures for consolidations problems, Computer Methods in Applied Mechanics and Engineering, 106, 51, 10.1016/0045-7825(93)90184-Y Tzschichholz, 1995, Simulations of pressure fluctuations and acoustic emission in hydraulic fracturing, Physical Review E, 5, 1961, 10.1103/PhysRevE.51.1961 Ulm, 2000, Thermo-chemo-mechanics of ASR expansion in concrete structures, Journal of Engineering Mechanics, 126, 233, 10.1061/(ASCE)0733-9399(2000)126:3(233) Vidic, 2013, Impact of shale gas development on regional water quality, Science, 340, 826, 10.1126/science.1235009 Vu-Bac, 2011, A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis, Computer Modeling in Engineering and Sciences, 73, 331 Watson, 1981, Computing the n-dimensional Delaunay tessellations with application to Voronoi polytopes, The Computer Journal, 24, 167, 10.1093/comjnl/24.2.167 Wells, 2001, A new method for modelling cohesive cracks using finiteelements, International Journal for Numerical Methods in Engineering, 50, 2667, 10.1002/nme.143 Wheeler, 2014, An augmented-Lagrangian method for the phase-field approach for pressurized fractures, Computer Methods in Applied Mechanics and Engineering, 271, 69, 10.1016/j.cma.2013.12.005 Winkler, 2001 Witek, 2007, Finite element analysis of various methods for protection of concrete structures against spalling during fire, Computational Mechanics, 39, 271, 10.1007/s00466-005-0024-7 Witherspoon, 1980, Validity of cubic law for fluid flow in a deformable rock fracture, Water Resources Research, 16, 1016, 10.1029/WR016i006p01016 Wyart, 2007, A substructured FE-shell/XFE-3D method for crack analysis in thin-walled structures, International Journal for Numerical Methods in Engineering, 72, 757, 10.1002/nme.2029 Xiao, 2006, Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery, International Journal for Numerical Methods in Engineering, 66, 1378, 10.1002/nme.1601 Xu, 1994, Numerical simulations of fast crack growth in brittle solids, Journal of the Mechanics and Physics of Solids, 42, 1397, 10.1016/0022-5096(94)90003-5 Zamani, 2010, Higher order tip enrichment of extended finite element method in thermoelasticity, Computational Mechanics, 46, 851, 10.1007/s00466-010-0520-2 Zapperi, 1999, Avalanches in breakdown and fracture processes, Physical Review E, 59, 5049, 10.1103/PhysRevE.59.5049 Zapperi, 1997, Plasticity and avalanche behavior in microfracturing phenomena, Nature, 388, 658, 10.1038/41737 Zeiml, 2008, Thermo-hydro-chemicalcouplings considered in safety assessment of shallow tunnels subjected to fire load, Fire Safety Journal, 43, 83, 10.1016/j.firesaf.2007.05.006 Zhu, 1988, Adaptive techniques in the finite element method, Communication in Applied Numerical Methods, 4, 197, 10.1002/cnm.1630040210 Zhou, 2004, Dynamic crack propagation with cohesive elements: A methodology to address mesh dependency, International Journal for Numerical Methods in Engineering, 59, 1, 10.1002/nme.857 Zhuang, 2011, Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling, International Journal for Numerical Methods in Engineering, 86, 249, 10.1002/nme.3063 Zhuang, 2012, Fracture modeling using meshless methods and level sets in 3D: Framework and modeling, International Journal for Numerical Methods in Engineering, 92, 969, 10.1002/nme.4365