A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 1-4, 2011, Pages 326-344

  Radovitzky, R ^a   Seagraves, A ^a   Tupek, M ^a   Noels, L ^b  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Cohesive zone models; Discontinuous Galerkin methods; Dynamic brittle fracture; Parallel computing

Indexed keywords

CERAMIC PLATES; CLOSED CRACK; COHESIVE ELEMENT; COHESIVE ELEMENT METHOD; COHESIVE ZONE MODEL; CONTINUUM PROBLEM; DISCONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN METHODS; DYNAMIC FRACTURES; FRACTURE PROCESS; INTERELEMENT BOUNDARIES; INTERFACE ELEMENTS; PARALLEL COMPUTATION; PARALLEL COMPUTING; SCALABLE ALGORITHMS; THREE DIMENSIONS; TOPOLOGICAL CHANGES; TRACTION-SEPARATION LAW; WAVE CHARACTERISTICS;

BRITTLENESS; CRACK CLOSURE; GALERKIN METHODS; PARALLEL ARCHITECTURES; STABILIZATION; TOPOLOGY; WAVE PROPAGATION;

BRITTLE FRACTURE;

EID: 78649635425     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.08.014     Document Type: Article

References (46)

1. Bowden F.P., Field J.E. The brittle fracture of solids by liquid impact, by solid impact and by shock. Proc. Roy. Soc. Lond. A 1964, 282:331-352.
2. Evans A.G., Wilshaw T.R. Dynamic solid particle damage in brittle materials, as appraisal. J. Mater. Sci. 1977, 12:97-116.
3. Evans A.G., Gulden M.E., Rosenblatt M. Impact damage in brittle materials in the elastic-plastic response regime. Proc. Roy. Soc. Lond. A 1978, 361:343-365.
4. Proceedings of the 32nd International Conference and Exposition on Advanced Ceramics and Composites. The American Ceramics Society 2008, Wiley, Daytone Beach, FL. L. Prokurat Franks (Ed.).
5. Council N.R. Protecting the Space Station from Meteoroids and Orbital Debris 1997, National Academy Press, Washington, DC.
6. Barenblatt G. The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 1962, 7:55-129.
7. Dugdale D. Yielding of steel sheets containing clits. J. Mech. Phys. Solids 1960, 8:100-104.
8. Seagraves A., Radovitzky R. Dynamic Failure of Materials and Structures. Advances in Cohesive Zone Modeling of Dynamic Fracture 2009, Springer, (Chapter 12).
9. Xu X., Needleman A. Numerical simulations of dynamic crack growth along an interface. Int. J. Fract. 1996, 74:289-324.
10. Xu X., Needleman A., Abraham F. Effect of inhomogeneities on dynamic crack growth in an elastic solid. Model. Simul. Mater. Sci. Engrg. 1997, 5:489-516.
11. Ruiz G., Pandolfi A., Ortiz M. Three-dimensional cohesive modeling of dynamic mixed-mode fracture. Int. J. Numer. Methods Engrg. 2001, 52(1-2):97-120.
12. Zhang Z., Paulino G., Celes W. Extrinsic cohesive modeling of dynamic fracture and microbranching instability in brittle materials. Int. J. Numer. Methods Engrg. 2007, 72:893-923.
13. Ortiz M., Suresh S. Statistical properties residual stresses and intergranular fracture in ceramic materials. J. Appl. Mech. 1993, 60:77-84.
14. Xu X., Needleman A. Numerical simulation of fast crack growth in brittle solids. J. Mech. Phys. Solids 1994, 42(9):1397-1434.
15. Espinosa H., Zavattieri P. A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part I: Theory and numerical implementation. Mech. Mater. 2003, 35:333-364.
16. Klein P., Foulk J., Chen E., Wimmer S., Gao H. Physics-based modeling of brittle fracture, cohesive formulations and the applications of meshfree methods. Theoret. Appl. Fract. Mech. 2001, 37:99-166.
17. Foulk J. An examination of stability in cohesive zone modeling. Comput. Methods Appl. Mech. Engrg. 2010, 199:465-470.
18. Camacho G., Ortiz M. Computational modeling of impact damage in brittle materials. Int. J. Solids Struct. 1996, 33(20-22):2899-2983.
19. Ortiz M., Pandolfi A. Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int. J. Numer. Methods Engrg. 1999, 44:1267-1282.
20. Nguyen O., Repetto E., Ortiz M., Radovitzky R. A cohesive model of fatigue crack growth. Int. J. Fract. 2001, 110:351-369.
21. Pandolfi A., Ortiz M. Solid modeling aspects of three-dimensional fragmentation. Engrg. Comput. 1998, 14:287-308.
22. Pandolfi A., Ortiz M. An efficient adaptive procedure for three-dimensional fragmentation simulations. Engrg. Comput. 2002, 18:148-159.
23. Mota A., Knap J., Ortiz M. Fracture and fragmentation of simplicial finite element meshes using graphs. Int. J. Numer. Methods Engrg. 2008, 73:1547-1570.
24. Paulino G., Celes W., Espinha R., Zhang Z. A general topology-based framework for adaptive insertion of cohesive elements in finite element meshes. Engrg. Comput. 2008, 24:59-78.
25. Dooley I., Mangala S., Kale L., Geubelle P. Parallel simulations of dynamic fracture using extrinsic cohesive elements. J. Sci. Comput. 2009, 39:144-165.
26. Ortiz M., Leroy Y., Needleman A. A finite element method for localized failure analysis. Comput. Methods Appl. Mech. Engrg. 1987, 61:189-214.
27. Dvorkin E., Cuitino A., Gioia G. Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions. Int. J. Numer. Methods Engrg. 1990, 30:541-564.
28. Armero F., Linder C. Numerical simulation of dynamic fracture using finite elements with embedded discontinuities. Int. J. Fract. 2009, 160:119-141.
29. Moes N., Dolbow J., Belytschko T. A finite element method for crack growth without remeshing. Int. J. Numer. Methods Engrg. 1999, 46:131-150.
30. Dolbow J., Moes N., Belytschko T. An extended finite element method for modeling crack growth with frictional contact. Comput. Methods Appl. Mech. Engrg. 2001, 190:6825-6846.
31. Areias P., Belytschko T. Analysis of three-dimensional crack initiation and propagation using the extended finite element method. Int. J. Numer. Methods Engrg. 2005, 63:760-788.
32. Remmers J., de Borst R., Needleman A. A cohesive segments method for the simulation of crack growth. Comput. Mech. 2003, 31:69-77.
33. de Borst R., Remmers J., Needleman A. Mesh-independent discrete numerical representations of cohesive-zone models. Engrg. Fract. Mech. 2006, 73:160-177.
34. Noels L., Radovitzky R. A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications. Int. J. Numer. Methods Engrg. 2006, 68(1):64-97.
35. Noels L., Radovitzky R. An explicit discontinuous Galerkin method for non-linear solid dynamics. Formulation, parallel implementation and scalability properties. Int. J. Numer. Methods Engrg. 2007, 74:1393-1420.
36. Mergheim J., Kuhl E., Steinmann P. A hybrid discontinuous Galerkin/interface method for the computational modelling of failure. Commun. Numer. Methods Engrg. 2004, 20:511-519.
37. Abedi R., Hawker M., Haber R., Matous K. An adaptive spacetime discontinuous Galerkin method for cohesive models of elastodynamic fracture. Int. J. Numer. Methods Engrg. 2009, 81:1207-1241.
38. Bassi F., Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 1997, 131:267-279.
39. Arnold D., Brezzi F., Cockburn B., Marini L. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 2002, 39(5):1749-1779.
40. Brezzi F., Manzini M., Marini D., Pietra P., Russo A. Discontinuous Galerkin approximations for elliptic problems. Numer. Methods Part. Differ. Equat. 2000, 16:47-58.
41. Belytschko T. Computational Methods for Transient Analysis 1983, Elsevier Science, North-Holland.
42. G. Karypis, V. Kumar, Analysis of multilevel graph partitioning, in: Proceedings of Supercomputing '95, San Diego, December 1995.
43. Radovitzky R., Ortiz M. Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation. Comput. Methods Appl. Mech. Engrg. 2000, 187:543-569.
44. Danielson K.T., Namburu R.R. Nonlinear dynamic finite element analysis on parallel computers using FORTRAN 90 and MPI. Adv. Engrg. Software 1998, 29:179-186.
45. Cummings J., Aivazis M., Samtaney R., Radovitzky R., Mauch S., Meiron D. A virtual test facility for the simulation of dynamic response in materials. J. Supercomput. 2002, 23:39-50.
46. Shockey D.A., Marchand A., Skaggs S., Cort G., Burkett M., Parker R. Failure phenomenology of confined ceramic targets and impacting rods. Int. J. Impact Engrg. 1990, 9(3):263-275.