Linear and nonlinear solvers for variational phase-field models of brittle fracture
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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
Griffith, 1921, The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society A, 221, 163, 10.1098/rsta.1921.0006
Francfort, 2008, The variational approach to fracture, Journal of Elasticity, 91, 5, 10.1007/s10659-007-9107-3
Ambrosio, 2000, Functions of Bounded Variations and Free Discontinuity Problems. Oxford Mathematical Monographs, 10.1093/oso/9780198502456.001.0001
Bourdin, 2000, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, 48, 787, 10.1016/S0022-5096(99)00028-9
Ambrosio, 1992, On the approximation of free discontinuity problems, Bollettino dell'Unione Matematica Italiana, 7, 105
Mumford, 1989, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, 42, 577, 10.1002/cpa.3160420503
Giacomini, 2005, Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures, Calculus of Variations and Partial Differential Equations, 22, 129, 10.1007/s00526-004-0269-6
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
Lorentz, 2011, Gradient damage models: toward full-scale computations, Computer Methods in Applied Mechanics and Engineering, 200, 1927, 10.1016/j.cma.2010.06.025
Pham, 2011, Gradient damage models and their use to approximate brittle fracture, International Journal of Damage Mechanics, 20, 618, 10.1177/1056789510386852
Bourdin, 2011, A time-discrete model for dynamic fracture based on crack regularization, International Journal of Fracture, 168, 133, 10.1007/s10704-010-9562-x
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
Schlüter, 2014, Phase field approximation of dynamic brittle fracture, Computational Mechanics, 54, 1, 10.1007/s00466-014-1045-x
Abdollahi, 2012, Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions, Journal of the Mechanics and Physics of Solids, 60, 2100, 10.1016/j.jmps.2012.06.014
Wheeler, 2014, An augmented-Lagrangian method for the phase-field approach for pressurized fractures, 4, 271, 69
Li, 2014, Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy, International Journal for Numerical Methods in Engineering, 102, 711, 10.1002/nme.4726
Del Piero, 2007, A variational model for fracture mechanics: numerical experiments, Journal of the Mechanics and Physics of Solids, 55, 2513, 10.1016/j.jmps.2007.04.011
Clayton, 2014, A geometrically nonlinear phase field theory of brittle fracture, International Journal of Fracture, 189, 1, 10.1007/s10704-014-9965-1
Hesch, 2014, Thermodynamically consistent algorithms for a finite-deformation phase-field approach to fracture, International Journal for Numerical Methods in Engineering, 99, 906, 10.1002/nme.4709
Verhoosel, 2013, A phase-field model for cohesive fracture, International Journal for Numerical Methods in Engineering, 96, 43, 10.1002/nme.4553
Amor, 2009, Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments, Journal of the Mechanics and Physics of Solids, 57, 1209, 10.1016/j.jmps.2009.04.011
Lancioni, 2009, The variational approach to fracture mechanics. A practical application to the French Panthéon in Paris, Journal of Elasticity, 95, 1, 10.1007/s10659-009-9189-1
Freddi, 2010, Regularized variational theories of fracture: a unified approach, Journal of the Mechanics and Physics of Solids, 58, 1154, 10.1016/j.jmps.2010.02.010
Ambati, 2015, A review on phase-field models of brittle fracture and a new fast hybrid formulation, Computational Mechanics, 55, 383, 10.1007/s00466-014-1109-y
Miehe, 2010, Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations, International Journal for Numerical Methods in Engineering, 83, 1273, 10.1002/nme.2861
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
Ambati, 2016, Phase-field modeling of brittle and ductile fracture in shells with isogeometric nurbs-based solid-shell elements, Computer Methods in Applied Mechanics and Engineering, 10.1016/j.cma.2016.02.017
Leon Baldelli, 2014, A variational model for fracture and debonding of thin films under in-plane loadings, Journal of the Mechanics and Physics of Solids, 70, 320, 10.1016/j.jmps.2014.05.020
Pham, 2011, The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models, Journal of the Mechanics and Physics of Solids, 59, 1163, 10.1016/j.jmps.2011.03.010
Pham, 2013, From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models, Continuum Mechanics and Thermodynamics, 25, 147, 10.1007/s00161-011-0228-3
Bourdin, 2014, Morphogenesis and propagation of complex cracks induced by thermal shocks, Physical Review Letters, 112, 014301, 10.1103/PhysRevLett.112.014301
Bourdin, 2007, Numerical implementation of the variational formulation for quasi-static brittle fracture, Interfaces and Free Boundaries, 9, 411, 10.4171/IFB/171
Miehe, 2010, 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
Facchinei, 1998, An active set Newton algorithm for large-scale nonlinear programs with box constraints, SIAM Journal on Optimization, 8, 158, 10.1137/S1052623493253991
Ulbrich, 2011, Semismooth Newton methods for variational inequalities and constrained optimization problems in function spaces, MOS-SIAM Series on Optimization, 11
Lorentz, 2004, A new path-following constraint for strain-softening finite element simulations, International Journal for Numerical Methods in Engineering, 60, 499, 10.1002/nme.971
Heister, 2015, A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach, Computer Methods in Applied Mechanics and Engineering, 290, 466, 10.1016/j.cma.2015.03.009
Singh, 2016, A fracture-controlled path-following technique for phase-field modeling of brittle fracture, Finite Elements in Analysis and Design, 113, 14, 10.1016/j.finel.2015.12.005
Gerasimov, A line search assisted monolithic approach for phase-field computing of brittle fracture, Computer Methods in Applied Mechanics and Engineering, 10.1016/j.cma.2015.12.017
Negri, 1999, The anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional, Numerical Functional Analysis and Optimization, 20, 957, 10.1080/01630569908816934
Bellettini, 1994, Discrete approximation of a free discontinuity problem, Numerical Functional Analysis and Optimization, 15, 105, 10.1080/01630569408816562
Burke, 2010, An adaptive finite element approximation of a variational model of brittle fracture, SIAM Journal on Numerical Analysis, 48, 980, 10.1137/080741033
Artina, 2015, Anisotropic mesh adaptation for crack detection in brittle materials, SIAM Journal on Scientific Computing, 37, B633-B659, 10.1137/140970495
Brune P Knepley MG Smith B Tu X Composing scalable nonlinear algebraic solvers. preprint ANL/MCS-P2010-0112, Argonne National Laboratory 2013
Ortega, 2000, Iterative Solution of Nonlinear Equations in Several Variables, 10.1137/1.9780898719468
Young DM Iterative methods for solving partial difference equations of elliptic type PhD Thesis Massachusetts, USA 1950
Arms, 1956, A method of block iteration, Journal of the Society for Industrial and Applied Mathematics, 4, 220, 10.1137/0104012
Kahan W Gauss-Seidel methods of solving large systems of linear equations PhD Thesis Ontario, Canada 1958
Ostrowski, 1954, On the linear iteration procedures for symmetric matrices, Rendiconti di Matematica e sue Applicazioni, 5, 140
Reid, 1966, A method for finding the optimum successive over-relaxation parameter, The Computer Journal, 9, 200, 10.1093/comjnl/9.2.200
Munson TS Algorithms and environments for complementarity PhD Thesis Wisconsin, USA 2000
Benson, 2006, Flexible complementarity solvers for large-scale applications, Optimization Methods and Software, 21, 155, 10.1080/10556780500065382
Fischer, 1992, A special Newton-type optimization method, Optimization, 24, 269, 10.1080/02331939208843795
Facchinei, 1997, A new merit function for nonlinear complementarity problems and a related algorithm, SIAM Journal on Optimization, 7, 225, 10.1137/S1052623494279110
Hestenes, 1952, Methods of conjugate gradients for solving linear systems, Journal of Research of the National Bureau of Standards, 49, 409, 10.6028/jres.049.044
Adams MF Bayraktar HH Keaveny TM Papadopoulos P Ultrascalable implicit finite element analyses in solid mechanics with over a half a billion degrees of freedom ACM/IEEE Proceedings of SC2004: High Performance Networking and Computing Pittsburgh, Pennsylvania 2004
Falgout, 2006, An introduction to algebraic multigrid computing, Computing in Science & Engineering, 8, 24, 10.1109/MCSE.2006.105
Hernandez, 2005, SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems, ACM Transactions on Mathematical Software, 31, 351, 10.1145/1089014.1089019
Vaněk, 1996, Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems, Computing, 56, 179, 10.1007/BF02238511
Gee M Siefert C Hu J Tuminaro R Sala M ML 5.0 smoothed aggregation user's guide. Technical Report SAND2006-2649 2006
Murphy, 2000, A note on preconditioning for indefinite linear systems, SIAM Journal on Scientific Computing, 21, 1969, 10.1137/S1064827599355153
Benzi, 2005, Numerical solution of saddle point problems, Acta Numerica, 14, 1, 10.1017/S0962492904000212
Brown J Knepley M May D McInnes L Smith B Composable linear solvers for multiphysics 2012 11th International Symposium on Parallel and Distributed Computing (ISPDC) Munich/Garching, Bavaria 2012 55 62
Balay S Abhyankar S Adams MF Brown J Brune P Buschelman K Eijkhout V Gropp WD Kaushik D Knepley MG et al PETSc users manual Technical Report ANL-95/11 - Revision 3.5 2014
Paige, 1975, Solution of sparse indefinite systems of linear equations, SIAM Journal on Numerical Analysis, 12, 617, 10.1137/0712047
Hossain, 2014, Effective toughness of heterogeneous media, Journal of the Mechanics and Physics of Solids, 71, 15, 10.1016/j.jmps.2014.06.002
Bahr, 1988, Multiple crack propagation in a strip caused by thermal shock, Theoretical and Applied Fracture Mechanics, 10, 219, 10.1016/0167-8442(88)90014-6
Jiang, 2012, A study of the mechanism of formation and numerical simulations of crack patterns in ceramics subjected to thermal shock, Acta Materialia, 60, 4540, 10.1016/j.actamat.2012.05.020
Sicsic, 2014, Initiation of a periodic array of cracks in the thermal shock problem: a gradient damage modeling, Journal of the Mechanics and Physics of Solids, 63, 256, 10.1016/j.jmps.2013.09.003
Amestoy, 2001, A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM Journal on Matrix Analysis and Applications, 23, 15, 10.1137/S0895479899358194
Eisenstat, 1996, Choosing the forcing terms in an inexact Newton method, SIAM Journal on Scientific Computing, 17, 16, 10.1137/0917003