Adaptive dynamic cohesive fracture simulation using nodal perturbation and edge‐swap operators

Dependence on mesh orientation impacts adversely the quality of computational solutions generated by cohesive zone models. For instance, when considering crack propagation along interfaces between finite elements of 4k structured meshes, both extension of crack length and crack angle are biased according to the mesh configuration. To address mesh orientation dependence in 4k structured meshes and to avoid undesirable crack patterns, we propose the use of nodal perturbation (NP) and edge-swap (ES) topological operation. To this effect, the topological data structure TopS (Int. J. Numer. Meth. Engng 2005; 64: 1529–1556), based on topological entities (node, element, vertex, edge and facet), is utilized so that it is possible to access adjacency information and to manage a consistent data structure in time proportional to the number of retrieved entities. In particular, the data structure allows the ES operation to be done in constant time. Three representative dynamic fracture examples using ES and NP operators are provided: crack propagation in the compact compression specimen, local branching instability, and fragmentation. These examples illustrate the features of the present computational framework in simulating a range of physical phenomena associated with cracking. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  Zhengyu Zhang,et al.  Extrinsic cohesive modeling of dynamic fracture and microbranching instability using a topological data structure , 2007 .

[2]  Leonidas J. Guibas,et al.  Randomized incremental construction of Delaunay and Voronoi diagrams , 1990, Algorithmica.

[3]  Mark S. Shephard,et al.  a General Topology-Based Mesh Data Structure , 1997 .

[4]  F. Erdogan,et al.  On the Crack Extension in Plates Under Plane Loading and Transverse Shear , 1963 .

[5]  Gross,et al.  Local crack branching as a mechanism for instability in dynamic fracture. , 1995, Physical review letters.

[6]  Pritam Ganguly,et al.  Spatial convergence of crack nucleation using a cohesive finite‐element model on a pinwheel‐based mesh , 2006 .

[7]  J. Molinari,et al.  Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency , 2004 .

[8]  Nicolas Moës,et al.  Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation , 2008 .

[9]  Glaucio H. Paulino,et al.  A compact adjacency‐based topological data structure for finite element mesh representation , 2005 .

[10]  Francisco Armero,et al.  Finite elements with embedded branching , 2009 .

[11]  M. Ortiz,et al.  FINITE-DEFORMATION IRREVERSIBLE COHESIVE ELEMENTS FOR THREE-DIMENSIONAL CRACK-PROPAGATION ANALYSIS , 1999 .

[12]  Charles Radin,et al.  The isoperimetric problem for pinwheel tilings , 1996 .

[13]  Glaucio H. Paulino,et al.  Integration of singular enrichment functions in the generalized/extended finite element method for three‐dimensional problems , 2009 .

[14]  G. Sih.  Strain-energy-density factor applied to mixed mode crack problems , 1974 .

[15]  Carlos Armando Duarte,et al.  A high‐order generalized FEM for through‐the‐thickness branched cracks , 2007 .

[16]  Anthony R. Ingraffea,et al.  Modeling mixed-mode dynamic crack propagation nsing finite elements: Theory and applications , 1988 .

[17]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[18]  Kyoungsoo Park,et al.  Potential-based fracture mechanics using cohesive zone and virtual internal bond modeling , 2009 .

[19]  Glaucio H. Paulino,et al.  Cohesive zone modeling of dynamic failure in homogeneous and functionally graded materials , 2005 .

[20]  M. Ortiz,et al.  Three‐dimensional cohesive modeling of dynamic mixed‐mode fracture , 2001 .

[21]  D. A. Field.  Laplacian smoothing and Delaunay triangulations , 1988 .

[22]  T. Belytschko,et al.  Extended finite element method for cohesive crack growth , 2002 .

[23]  Glaucio H. Paulino,et al.  Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials , 2007 .

[24]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

[25]  Glaucio H. Paulino,et al.  A general topology-based framework for adaptive insertion of cohesive elements in finite element meshes , 2008, Engineering with Computers.

[26]  L. J. Sluys,et al.  A new method for modelling cohesive cracks using finite elements , 2001 .

[27]  Luiz Velho,et al.  Variable Resolution 4‐k Meshes: Concepts and Applications , 2000, Comput. Graph. Forum.

[28]  Joseph E. Bishop,et al.  Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations , 2009 .

[29]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

[30]  Pritam Ganguly,et al.  An Algorithm for Two-Dimensional Mesh Generation Based on the Pinwheel Tiling , 2004, SIAM J. Sci. Comput..

[31]  Glaucio H. Paulino,et al.  Efficient Handling of Implicit Entities in Reduced Mesh Representations , 2005, J. Comput. Inf. Sci. Eng..

[32]  Glaucio H. Paulino,et al.  A unified potential-based cohesive model of mixed-mode fracture , 2009 .

[33]  Brodbeck,et al.  Instability dynamics of fracture: A computer simulation investigation. , 1994, Physical review letters.

[34]  J. W. Foulk,et al.  Physics-based Modeling of Brittle Fracture: Cohesive Formulations and the Application of Meshfree Methods , 2000 .

[35]  Francisco Armero,et al.  Finite elements with embedded strong discontinuities for the modeling of failure in solids , 2007 .

[36]  George A. Gazonas,et al.  The cohesive element approach to dynamic fragmentation: the question of energy convergence , 2007 .

[37]  Hubert Maigre,et al.  An investigation of dynamic crack initiation in PMMA , 1996 .

[38]  P. Krysl,et al.  Finite element simulation of ring expansion and fragmentation: The capturing of length and time scales through cohesive models of fracture , 1999 .

[39]  Daniel P. Huttenlocher,et al.  Comparing Images Using the Hausdorff Distance , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[40]  Huajian Gao,et al.  Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds , 1998 .

[41]  S. H. Lo,et al.  Generating quadrilateral elements on plane and over curved surfaces , 1989 .

[42]  T. Belytschko,et al.  Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment , 2003 .

[43]  L. B. Freund,et al.  Energy dissipation in dynamic fracture of brittle materials , 1999 .

[44]  Ted Belytschko,et al.  Cracking particles: a simplified meshfree method for arbitrary evolving cracks , 2004 .

[45]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[46]  Ted Belytschko,et al.  Cracking node method for dynamic fracture with finite elements , 2009 .

[47]  J. Fineberg,et al.  Microbranching instability and the dynamic fracture of brittle materials. , 1996, Physical review. B, Condensed matter.

[48]  Stephen A. Vavasis,et al.  Time continuity in cohesive finite element modeling , 2003 .