Cracking node method for dynamic fracture with finite elements.

*(English)*Zbl 1155.74415Summary: A new method for modeling discrete cracks based on the extended finite element method is described. In the method, the growth of the actual crack is tracked and approximated with contiguous discrete crack segments that lie on finite element nodes and span only two adjacent elements. The method can deal with complicated fracture patterns because it needs no explicit representation of the topology of the actual crack path. A set of effective rules for injection of crack segments is presented so that fracture behavior beginning from arbitrary crack nucleations to macroscopic crack propagation is seamlessly modeled. The effectiveness of the method is demonstrated with several dynamic fracture problems that involve complicated crack patterns such as fragmentation and crack branching.

PDF
BibTeX
XML
Cite

\textit{J.-H. Song} and \textit{T. Belytschko}, Int. J. Numer. Methods Eng. 77, No. 3, 360--385 (2009; Zbl 1155.74415)

Full Text:
DOI

##### References:

[1] | Swenson, Modelling mixed-mode dynamic crack propagation using finite elements: theory and applications, Computational Mechanics 3 pp 187– (1988) · Zbl 0663.73074 |

[2] | Martha, Arbitrary crack representation using solid modeling, Engineering with Computers 9 pp 63– (1993) |

[3] | Belytschko, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering 45 (5) pp 601– (1999) · Zbl 0943.74061 |

[4] | Moës, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46 (1) pp 131– (1999) · Zbl 0955.74066 |

[5] | Babuška, The partition of unity method, International Journal for Numerical Methods in Engineering 40 (4) pp 727– (1997) |

[6] | Stolarska, Modeling crack growth by level sets in the extended finite element method, International Journal for Numerical Methods in Engineering 51 (8) pp 943– (2001) · Zbl 1022.74049 |

[7] | Belytschko, Arbitrary discontinuities in finite elements, International Journal for Numerical Methods in Engineering 50 (4) pp 993– (2001) · Zbl 0981.74062 |

[8] | Ventura, A vector level set method and new discontinuity approximations for crack growth by EFG, International Journal for Numerical Methods in Engineering 54 pp 923– (2002) · Zbl 1034.74053 |

[9] | Ventura, Vector level sets for description of propagating cracks in finite elements, International Journal for Numerical Methods in Engineering 58 pp 1571– (2003) · Zbl 1032.74687 |

[10] | Prabel, Level set X-FEM non-matching meshes: application to dynamic crack propagation in elastic-plastic media, International Journal for Numerical Methods in Engineering 69 pp 1553– (2007) · Zbl 1194.74465 |

[11] | Areias, Analysis of three-dimensional crack initiation and propagation using the extended finite element method, International Journal for Numerical Methods in Engineering 63 pp 760– (2005) · Zbl 1122.74498 |

[12] | Belytschko, Dynamic crack propagation based on loss of hyperbolicity with a new discontinuous enrichment, International Journal for Numerical Methods in Engineering 58 pp 1873– (2003) · Zbl 1032.74662 |

[13] | Zi, A new method for multiple cracks and its application to fatigue crack growth, Modeling and Simulations in Materials Science and Engineering 12 pp 901– (2004) |

[14] | Song, A method for dynamic crack and shear band propagation with phantom nodes, International Journal for Numerical Methods in Engineering 67 pp 868– (2006) · Zbl 1113.74078 |

[15] | Areias, A finite-strain quadrilateral shell element based on discrete Kirchhoff-Love constraints, International Journal for Numerical Methods in Engineering 64 pp 1166– (2005) · Zbl 1113.74063 |

[16] | Areias, Analysis of fracture in thin shells by overlapping paired elements, Computer Methods in Applied Mechanics and Engineering 195 pp 5343– (2006) · Zbl 1120.74048 |

[17] | Song, Dynamic fracture of shells subjected to impulsive loads, Journal of Applied Mechanics (2008) |

[18] | Fish, The s-version of the finite element method, Computers and Structures 43 (3) pp 539– (1992) · Zbl 0775.73247 |

[19] | Belytschko, Efficient large-scale nonlinear transient analysis finite-elements, International Journal for Numerical Methods in Engineering 10 pp 579– (1976) |

[20] | Xu, Numerical simulation of fast crack growth in brittle solids, Journal of the Mechanics and Physics of Solids 42 (9) pp 1397– (1994) · Zbl 0825.73579 |

[21] | Camacho, Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures 33 pp 2899– (1996) · Zbl 0929.74101 |

[22] | Belytschko, A finite element with embedded localization zones, Computer Methods in Applied Mechanics and Engineering 70 pp 59– (1988) · Zbl 0653.73032 |

[23] | Strouboulis, The design and analysis of generalized finite element method, Computer Methods in Applied Mechanics and Engineering 181 pp 43– (2000) · Zbl 0983.65127 |

[24] | Duarte, Generalized finite element methods for three-dimensional structural mechanics problems, Computers and Structures 77 pp 215– (2000) |

[25] | Duarte, High-order generalized FEM for through-the-thickness branched cracks, International Journal for Numerical Methods in Engineering 72 pp 325– (2007) · Zbl 1194.74385 |

[26] | Ortiz, Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, International Journal for Numerical Methods in Engineering 44 pp 1267– (1999) · Zbl 0932.74067 |

[27] | Papoulia, Time continuity in cohesive finite element modeling, International Journal for Numerical Methods in Engineering 58 pp 679– (2003) · Zbl 1032.74676 |

[28] | Papoulia, Spatial convergence of crack nucleation using a cohesive finite-element model on a pinwhell-based mesh, International Journal for Numerical Methods in Engineering 67 pp 1– (2006) · Zbl 1110.74854 |

[29] | Song, A comparative study on finite element methods for dynamic fracture, Computational Mechanics · Zbl 1160.74048 · doi:10.1007/s00466-007-0210-x |

[30] | Zavattieri, Grain level analysis of crack initiation and propagation in brittle materials, Acta Materialia 49 pp 4291– (2001) |

[31] | Zhou, Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency, International Journal for Numerical Methods in Engineering 59 pp 1– (2004) · Zbl 1047.74074 |

[32] | Dvorkin, Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions, International Journal for Numerical Methods in Engineering 30 pp 541– (1990) · Zbl 0729.73209 |

[33] | Simo, An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, International Journal for Numerical Methods in Engineering 12 pp 277– (1993) · Zbl 0783.73024 |

[34] | Armero, An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids, International Journal of Solids and Structures 33 pp 2863– (1996) · Zbl 0924.73084 |

[35] | Jirásek, Comparative study on finite elements with embedded discontinuities, Computer Methods in Applied Mechanics and Engineering 188 pp 307– (2000) · Zbl 1166.74427 |

[36] | Fan, The rs-method for material failure simulations, International Journal for Numerical Methods in Engineering 73 pp 1607– (2008) · Zbl 1159.74039 |

[37] | Remmers, A cohesive segments method for the simulation of crack growth, Computational Mechanics 31 pp 69– (2003) · Zbl 1038.74679 |

[38] | de Borst, Mesh-independent discrete numerical representations of cohesive-zone models, Engineering Fracture Mechanics 73 pp 160– (2006) |

[39] | Rabczuk, Cracking particles: a simplified meshfree method for arbitrary evolving cracks, International Journal for Numerical Methods in Engineering 61 pp 2316– (2004) · Zbl 1075.74703 |

[40] | Rabczuk, A simplified meshfree method for shear bands with cohesive surfaces, International Journal for Numerical Methods in Engineering 69 pp 993– (2007) · Zbl 1194.74536 |

[41] | Rabczuk, Discontinuous modelling of shear bands using adaptive meshfree methods, Computer Methods in Applied Mechanics and Engineering 107 pp 641– (2008) · Zbl 1169.74655 · doi:10.1016/j.cma.2007.08.027 |

[42] | Belytschko, Nonlinear Finite Elements for Continua and Structures (2000) |

[43] | Flanagan, A uniform strain hexahedron and quadrilateral with orthogonal hourglass control, International Journal for Numerical Methods in Engineering 17 pp 679– (1981) · Zbl 0478.73049 |

[44] | Daniel, Suppression of spurious intermediate frequency modes in under-integrated elements by combined stiffness/viscous stabilization, International Journal for Numerical Methods in Engineering 64 pp 335– (2005) · Zbl 1181.74134 |

[45] | Menouillard, Efficient explicit time stepping for the extended finite element method, International Journal for Numerical Methods in Engineering 68 pp 911– (2006) · Zbl 1128.74045 |

[46] | Menouillard, Mass lumping strategies for X-FEM explicit dynamics: application to crack propagation, International Journal for Numerical Methods in Engineering (2007) · Zbl 1159.74432 · doi:10.1002/nme.2180 |

[47] | Kalthoff, Failure mode transition at high rates of shear loading, International Conference on Impact Loading and Dynamic Behavior of Materials 1 pp 185– (1987) |

[48] | Lee, Fracture initiation due to asymmetric impact loading of an edge cracked plate, Journal of Applied Mechanics 57 pp 104– (1990) |

[49] | Kalthoff, Modes of dynamic shear failure in solids, International Journal of Fracture 101 pp 1– (2000) |

[50] | Decker, Source Book on Maraging Steels (1979) |

[51] | Belytschko, Dynamic fracture using element-free Galerkin methods, International Journal for Numerical Methods in Engineering 39 pp 923– (1996) · Zbl 0953.74077 |

[52] | Réthoré, An energy-conserving scheme for dynamic crack growth using the extended finite element method, International Journal for Numerical Methods in Engineering 63 pp 631– (2005) · Zbl 1122.74519 |

[53] | Ramulu, Mechanics of crack curving and branching-a dynamic fracture analysis, International Journal of Fracture 27 pp 187– (1985) |

[54] | Satoh H. On the crack propagation in brittle materials. Ph.D. Thesis, University of Tokyo, Japan, 1996. |

[55] | Ravi-Chandar, Dynamic fracture of nominally brittle materials, International Journal of Fracture 90 pp 83– (1998) |

[56] | Sharon, Microbranching instability and the dynamic fracture of brittle materials, Physical Review B 54 (10) pp 7128– (1996) |

[57] | Sharon, Energy dissipation in dynamic fracture, Physical Review Letters 76 (12) pp 2117– (1996) |

[58] | Sharon, Confirming the continuum theory of dynamic brittle fracture for fast cracks, Letters to Nature 397 pp 333– (1999) |

[59] | Rabczuk, Simulations of instability in dynamic fracture by the cracking particles method, Engineering Fracture Mechanics (2008) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.