A phase-field description of dynamic brittle fracture

Computer Methods in Applied Mechanics and Engineering - Tập 217-220 - Trang 77-95 - 2012
Michael J. Borden1, Clemens V. Verhoosel2, Michael A. Scott1, Thomas J.R. Hughes1, Chad M. Landis3
1Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station C0200, Austin, TX 78712, USA
2Eindhoven University of Technology, Mechanical Engineering, Numerical Methods in Engineering, PO Box 513, WH 2.115, 5600 MB Eindhoven, The Netherlands
3Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, 1 University Station C0600, Austin, TX 78712, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Ambrosio, 1990, Approximation of functional depending on jumps by elliptic functional via Γ-convergence, Commun. Pure Appl. Math., 43, 999, 10.1002/cpa.3160430805

Ambrosio, 1992, On the approximation of free discontinuity problems, Boll. Un. Mat. Ital. B (7), 6, 105

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

Babuška, 1997, The partition of unity method, Int. J. Numer. Methods Engrg., 40, 727, 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N

Bellettini, 1994, Discrete approximation of a free discontinuity problem, Numer. Funct. Anal. Optim., 15, 201, 10.1080/01630569408816562

Belytschko, 2003, Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment, Int. J. Numer. Methods Eng., 58, 1873, 10.1002/nme.941

Benallal, 2007, Bifurcation and stability issues in gradient theories with softening, Modell. Simul. Mater. Sci. Engrg., 15, S283, 10.1088/0965-0393/15/1/S22

Benson, 1998, Stable time step estimation for multi-material eulerian hydrocodes, Comput. Methods Appl. Mech. Engrg., 167, 191, 10.1016/S0045-7825(98)00119-4

Benson, 2011, A large deformation, rotation-free, isogeometric shell, Comput. Methods Appl. Mech. Engrg., 200, 1367, 10.1016/j.cma.2010.12.003

Borden, 2011, Isogeometric finite element data structures based on Bézier extraction of NURBS, Int. J. Numer. Methods Engrg., 87, 15, 10.1002/nme.2968

Bourdin, 1999, Image segmentation with a finite element method, M2AN Math. Modell. Numer. Anal., 33, 229, 10.1051/m2an:1999114

Bourdin, 2007, Numerical implementation of the variational formulation for quasi-static brittle fracture, Interf. Free Bound., 9, 411, 10.4171/IFB/171

Bourdin, 2000, Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, 48, 797, 10.1016/S0022-5096(99)00028-9

Bourdin, 2008, The variational approach to fracture, J. Elast., 91, 5, 10.1007/s10659-007-9107-3

Bourdin, 2011, A time-discrete model for dynamic fracture based on crack regularization, Int. J. Fract., 168, 133, 10.1007/s10704-010-9562-x

Braides, 1998

Burke, 2010, An adaptive finite element approximation of a variational model of brittle fracture, SIAM J. Numer. Anal., 48, 980, 10.1137/080741033

Chung, 1993, A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-alpha method, J. Appl. Mech., 60, 371, 10.1115/1.2900803

Del Piero, 2007, A variational model for fracture mechanics: numerical experiments, J. Mech. Phys. Solids, 55, 2513, 10.1016/j.jmps.2007.04.011

Francfort, 2009, Critical points of Ambrosio–Tortorelli converge to critical points of Mumford–Shah in the one-dimensional Dirichlet case, ESAIM: Control Optim. Calc. Var., 15, 576

Francfort, 1998, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46, 1319, 10.1016/S0022-5096(98)00034-9

Giacomini, 2005, Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures, Calc. Var. Partial Diff. Equat., 22, 129, 10.1007/s00526-004-0269-6

Hilber, 1977, Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Engrg. Struct. Dyn., 5, 283, 10.1002/eqe.4290050306

Hughes, 2000

Hughes, 2005, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 4135, 10.1016/j.cma.2004.10.008

Hughes, 2008, Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS, Comput. Methods Appl. Mech. Engrg., 197, 4104, 10.1016/j.cma.2008.04.006

Hughes, 2010, Efficient quadrature for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 199, 301, 10.1016/j.cma.2008.12.004

Hulbert, 1996, Explicit time integration algorithms for structural dynamics with optimal numerical dissipation, Comput. Methods Appl. Mech. Engrg., 137, 175, 10.1016/S0045-7825(96)01036-5

Kalthoff, 2000, Modes of dynamic shear failure in solids, Int. J. Fract., 101, 1, 10.1023/A:1007647800529

J.F. Kalthoff, S. Winkler. Failure mode transition of high rates of shear loading, in: C.Y. Chiem, H.D. Kunze, L.W. Meyer, (Eds.), Proceedings of the International Conference on Impact Loading and Dynamic Behavior of Materials, vol. 1, 1987, pp. 185–195.

Karma, 2001, Phase-field model of mode III dynamic fracture, Phys. Rev. Lett., 87, 045501, 10.1103/PhysRevLett.87.045501

Krueger, 2004, Virtual crack closure technique: history, approach, and applications, Appl. Mech. Rev., 57, 109, 10.1115/1.1595677

Lancioni, 2009, The variational approach to fracture mechanics. a practical application to the French Panthéon in Paris, J. Elast., 95, 1, 10.1007/s10659-009-9189-1

Larsen, 2010, Models for dynamic fracture based on griffith’s criterion, vol. 21, 131

Larsen, 2010, Existence of solutions to a regularized model of dynamic fracture, Math. Methods Models Appl. Sci., 20, 1021, 10.1142/S0218202510004520

Li, 2012, On linear independence of T-splines blending functions, Comput. Aided Geometric Des., 29, 63, 10.1016/j.cagd.2011.08.005

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, 2010, Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations, Int. J. Numer. Methods Engrg., 83, 1273, 10.1002/nme.2861

Miranda, 1989, An improved implicit-explicit time integration method for structural dynamics, Earthquake Engrg. Struct. Dyn., 18, 643, 10.1002/eqe.4290180505

Moës, 1999, A finite element method for crack growth without remeshing, Int. J. Numer. Methods Engrg., 46, 131, 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J

Mumford, 1989, Optimal approximations by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math., 42, 577, 10.1002/cpa.3160420503

Pham, 2011, Gradient damage models and their use to approximate brittle fracture, Int. J. Damage Mech., 20, 618, 10.1177/1056789510386852

Pham, 2009, Construction and analysis of localized responses for gradient damage models in a 1d setting, Vietnam J. Mech., 31, 233, 10.15625/0866-7136/31/3-4/5651

Piegl, 1997, 10.1007/978-3-642-59223-2

Ravi-Chandar, 1998, Dynamic fracture of nominally brittle materials, Int. J. Fract., 90, 83, 10.1023/A:1007432017290

Ravi-Chandar, 1984, An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching, Int. J. Fract., 26, 141, 10.1007/BF01157550

Ravi-Chandar, 2000, Failure mode transitions in polymers under high strain rate loading, Int. J. Fract., 101, 33, 10.1023/A:1007581101315

Remmers, 2008, The simulation of dynamic crack propagation using the cohesive segments method, J. Mech. Phys. Solids, 56, 70, 10.1016/j.jmps.2007.08.003

Scott, 2011, Isogeometric finite element data structures based on Bézier extraction of T-splines, Int. J. Numer. Methods Engrg., 88, 126, 10.1002/nme.3167

Scott, 2012, Local refinement of analysis-suitable T-splines, Comput. Methods Appl. Mech. Engrg., 213–216, 206, 10.1016/j.cma.2011.11.022

Song, 2008, A comparative study on finite element methods for dynamic fracture, Comput. Mech., 42, 239, 10.1007/s00466-007-0210-x

Verhoosel, 2011, An isogeometric approach to cohesive zone modeling, Int. J. Numer. Methods Engrg., 88, 336, 10.1002/nme.3061

Verhoosel, 2011, An isogeometric analysis approach to gradient damage models, Int. J. Numer. Methods Engrg., 86, 115, 10.1002/nme.3150