journal article·2012-11Open access

Validation tests of the full-discontinuous Galerkin/extrinsic cohesive law framework of Kirchhoff-Love shells

Gauthier Becker, Ludovic Noels

International Journal of Fracture· Volume 178· Issue 1-2

Abstract

Due to its ability to account for discontinuities, the discontinuous Galerkin (DG) method presents two main advantages for modeling crack initiations and propagation. On the one hand, it provides an easy way to insert the cohesive elements during the simulation and therefore avoids the drawbacks inherent to the use of an extrinsic cohesive law. On the other hand, the capture of complex crack path requires very thin meshes, and the recourse to a parallel implementation of DG formulations exhibits a high scalability of the resolution scheme. Recently, the authors developed such a DG-fracture framework for Kirchhoff-Love shells in the linear and non-linear ranges. They proved that this framework dissipates, during the fracture process, an amount of energy equal to the fracture energy of the material and that the model is able to propagate the crack with the right speed. In this paper, novel numerical benchmarks are presented to validate the method in various fracture conditions. The two first ones include an initial notch and study the fracture propagation under two different dynamic loadings (impact and blast). The two other ones focus on the fragmentation of initially unbroken specimens due to uniform expansion, in order to demonstrate the ability of the new framework to model crack initiations. Results are in all cases in agreement with the ones reported in the literature.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Numerical methods in engineering · Fluid Dynamics Simulations and Interactions · Mechanical Behavior of Composites

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (63)

Show source-provided references
1. Barsoum I, Faleskog J (2007) Rupture mechanisms in combined tension and shearmicromechanics. Int J Solids Struct 44(17): 5481–5498. doi: 10.1016/j.ijsolstr.2007.01.01010.1016/j.ijsolstr.2007.01.010 ↗
2. Becker G, Noels L (2011) A fracture framework for euler-bernoulli beams based on a full discontinuous galerkin formulation/extrinsic cohesive law combination. Int J Numer Methods Eng 85(10): 1227–1251. doi: 10.1002/nme.300810.1002/nme.3008 ↗
3. Becker G, Noels L (2012) A full discontinuous galerkin formulation of non-linear kirchhoff-love shells: elasto-plastic finite deformations, parallel computation & fracture applications. Int J Numer Methods Eng. doi: 10.1002/nme.438110.1002/nme.4381 ↗
4. Becker G, Geuzaine C, Noels L (2011) A one field full discontinuous galerkin method for kirchhoff-love shells applied to fracture mechanics. Comput Methods Appl Mech Eng 200(45–46): 3223–3241. doi: 10.1016/j.cma.2011.07.00810.1016/j.cma.2011.07.008 ↗
5. Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33(20-22):2899–2938. http://www.sciencedirect.com/science/article/B6VJS-3VTSPVJ-3/2/98fe3c31d0cee8e029d78d1631c6bbdd10.1016/0020-7683(95)00255-3 ↗
6. Cirak F, Ortiz M (2001) Fully c1-conforming subdivision elements for finite deformation thin-shell analysis. Int J Numer Methods Eng 51(7): 813–833. doi: 10.1002/nme.18210.1002/nme.182.abs ↗
7. Cirak F, Ortiz M, Schröder P (2000) Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. Int J Numer Methods Eng 47(12): 2039–2072. doi: 10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-110.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1 ↗
8. Cirak F, Ortiz M, Pandolfi A (2005) A cohesive approach to thin-shell fracture and fragmentation. Comput Methods Appl Mech Eng 194(21-24):2604–2618. http://www.sciencedirect.com/science/article/B6V29-4FBW600-4/2/06c015e841d7fba329790dd872c4986e10.1016/j.cma.2004.07.048 ↗
9. Corigliano A, Cacchione F, Frangi A, Zerbini S (2008) Numerical modelling of impact rupture in polysilicon microsystems. Comput Mech 42: 251–259. doi: 10.1007/s00466-007-0231-510.1007/s00466-007-0231-5 ↗
10. Cuitino A, Ortiz M (1992) A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics. Eng Comput 9: 437–45110.1108/eb023876 ↗
11. Deiterding R, Radovitzky R, Mauch S, Noels L, Cummings J, Meiron D (2006) A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading. Eng Comput 22(3): 325–347. doi: 10.1007/s00366-006-0043-910.1007/s00366-006-0043-9 ↗
12. Dickens SH, Cho BH (2005) Interpretation of bond failure through conversion and residual solvent measurements and weibull analyses of flexural and microtensile bond strengths of bonding agents. Dental Mater 21(4): 354–364. doi: 10.1016/j.dental.2004.05.00710.1016/j.dental.2004.05.007 ↗
13. Dung NT, Wells GN (2008) Geometrically nonlinear formulation for thin shells without rotation degrees of freedom. Comput Methods Appl Mech Eng 197(3340): 2778–2788. doi: 10.1016/j.cma.2008.01.00110.1016/j.cma.2008.01.001 ↗
14. Engel G, Garikipati K, Hughes TJR, Larson MG, Mazzei L, Taylor RL (2002) Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity. Comput Methods Appl Mech Eng 191(34):3669–3750. http://www.sciencedirect.com/science/article/B6V2-45SRHD8-1/2/464ae949db39e8ad8352b2319505110910.1016/S0045-7825(02)00286-4 ↗
15. Gao X, Kim J (2006) Modeling of ductile fracture: significance of void coalescence. Int J Solids Struct 43(20): 6277–6293. doi: 10.1016/j.ijsolstr.2005.08.00810.1016/j.ijsolstr.2005.08.008 ↗
16. Hansbo P, Larson MG, Hillerborg A, Modéer M, Petersson PE, Larsson R, Mediavilla J, Fagerström M (2002) A discontinuous galerkin method for the plate equation. Calcolo 39(1): 41–59. doi: 10.1007/s10092020000110.1007/s100920200001 ↗
17. Hillerborg A, Modéer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6(6): 773–781. doi: 10.1016/0008-8846(76)90007-710.1016/0008-8846(76)90007-7 ↗
18. Hulbert GM, Chung J (1996) Explicit time integration algorithms for structural dynamics with optimal numerical dissipation. Comput Methods Appl Mech Eng 137(2):175–188. doi: 10.1016/S0045-7825(96)01036-5 . http://www.sciencedirect.com/science/article/B6V29-3WFNRDY-5/2/2ec79b924e3dd1b9231ffe40c6a4030610.1016/S0045-7825(96)01036-5 ↗
19. Larsson R, Mediavilla J, Fagerström M (2011) Dynamic fracture modeling in shell structures based on xfem. Int J Numer Meth Eng 86(4–5): 499–527. doi: 10.1002/nme.308610.1002/nme.3086 ↗
20. Leterrier Y, Andersons J, Pitton Y, Manson JAE (1997) Adhesion of silicon oxide layers on poly(ethylene terephthalate). ii: effect of coating thickness on adhesive and cohesive strengths. J Polym Sci Part B Polym Phys 35(9): 1463–1472. doi: 10.1002/(SICI)1099-0488(19970715)35:9<1463::AID-POLB16>3.0.CO;2-410.1002/(SICI)1099-0488(19970715)35:9<1463::AID-POLB16>3.0.CO;2-4 ↗
21. Levy S (2010) Exploring the physics behind dynamic fragmentation through parallel simulations. PhD thesis, Ecole Polytechnique Fédérale de Lausanne, Lausanne. doi: 10.5075/epfl-thesis-4898 . http://library.epfl.ch/theses/?nr=4898
22. Levy S, Molinari J, Radovitzky R (2012) Dynamic fragmentation of a brittle plate under biaxial loading: strength or toughness controlled. Int J Fract 174: 203–215. doi: 10.1007/s10704-012-9691-510.1007/s10704-012-9691-5 ↗
23. Li H, Chandra N (2003) Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models. Int J Plast 19(6):849-882. http://www.sciencedirect.com/science/article/B6TWX-45DF7DC-2/2/5b0f96fbff717dba3403fe5e02295e4610.1016/S0749-6419(02)00008-6 ↗
24. Mergheim J, Kuhl E, Steinmann P (2004) A hybrid discontinuous galerkin/interface method for the computational modelling of failure. Commun Numer Methods Eng 20(7): 511–519. doi: 10.1002/cnm.68910.1002/cnm.689 ↗
25. Molinari JF, Gazonas G, Raghupathy R, Rusinek A, Zhou F (2007) The cohesive element approach to dynamic fragmentation: the question of energy convergence. Int J Numer Methods Eng 69(3): 484–503. doi: 10.1002/nme.177710.1002/nme.1777 ↗
26. Mota A, Knap J, Ortiz M (2008) Fracture and fragmentation of simplicial finite element meshes using graphs. Int J Numer Methods Eng 73(11): 1547–1570. doi: 10.1002/nme.213510.1002/nme.2135 ↗
27. Nahshon K, Hutchinson J (2008) Modification of the gurson model for shear failure. Eur J Mech A Solids 27(1): 1–17. doi: 10.1016/j.euromechsol.2007.08.00210.1016/j.euromechsol.2007.08.002 ↗
28. Needleman A (1987) A continuum model for void nucleation by inclusion debonding. J Appl Mech 54: 525–53110.1115/1.3173064 ↗
29. Needleman A (1990a) An analysis of decohesion along an imperfect interface. Int J Fract 42: 21–40. doi: 10.1007/BF0001861110.1007/BF00018611 ↗
30. Needleman A (1990) An analysis of tensile decohesion along an interface. J Mech Phys Solids 38(3): 289–324. doi: 10.1016/0022-5096(90)90001-K10.1016/0022-5096(90)90001-K ↗
31. Nielsen K, Hutchinson J (2011) Cohesive traction-separation laws for tearing of ductile metal plates. Int J Impact Eng. doi: 10.1016/j.ijimpeng.2011.02.00910.1016/j.ijimpeng.2011.02.009 ↗
32. Nielsen KL, Tvergaard V (2009) Effect of a shear modified gurson model on damage development in a fsw tensile specimen. Int J Solids Struct 46(34): 587–601. doi: 10.1016/j.ijsolstr.2008.09.01110.1016/j.ijsolstr.2008.09.011 ↗
33. Noels L (2009) A discontinuous galerkin formulation of non-linear kirchhoff-love shells. Int J Numer Methods Eng 78(3): 296–323. doi: 10.1002/nme.248910.1002/nme.2489 ↗
34. Noels L, Radovitzky R (2008) A new discontinuous galerkin method for kirchhoff-love shells. Comput Methods Appl Mech Eng 197(33-40):2901–2929. http://www.sciencedirect.com/science/article/B6V29-4RSRDCT-1/2/9b24e4b7bb547bf5c27d28e6b089861010.1016/j.cma.2008.01.018 ↗
35. Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44: 1267–1282. doi: 10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-710.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7 ↗
36. Pandolfi A, Ortiz M (2002) An efficient adaptive procedure for three-dimensional fragmentation simulations. Eng Comput 18(2): 148–159. doi: 10.1007/s00366020001310.1007/s003660200013 ↗
37. Pandolfi A, Guduru P, Ortiz M, Rosakis A (2000) Three dimensional cohesive-element analysis and experiments of dynamic fracture in c300 steel. Int J Solids Struct 37(27): 3733–3760. doi: 10.1016/S0020-7683(99)00155-910.1016/S0020-7683(99)00155-9 ↗
38. Papoulia KD, Sam CH, Vavasis SA (2003) Time continuity in cohesive finite element modeling. Int J Numer Methods Eng 58(5): 679–701. doi: 10.1002/nme.77810.1002/nme.778 ↗
39. Papoulia KD, Vavasis SA, Ganguly P (2006) Spatial convergence of crack nucleation using a cohesive finite-element model on a pinwheel-based mesh. Int J Numer Methods Eng 67(1): 1–16. doi: 10.1002/nme.159810.1002/nme.1598 ↗
40. Prechtel M, Leugering G, Steinmann P, Stingl M (2011) Towards optimization of crack resistance of composite materials by adjustment of fiber shapes. Eng Fract Mech 78(6): 944–960. doi: 10.1016/j.engfracmech.2011.01.00710.1016/j.engfracmech.2011.01.007 ↗
41. Radovitzky R, Seagraves A, Tupek M, Noels L (2011) A scalable 3d fracture and fragmentation algorithm based on a hybrid, discontinuous galerkin, cohesive element method. Comput Methods Appl Mech Eng 200(1–4): 326–344. doi: 10.1016/j.cma.2010.08.01410.1016/j.cma.2010.08.014 ↗
42. Scheider I, Brocks W (2003) Simulation of cup-cone fracture using the cohesive model. Eng Fract Mech 70(14): 1943–1961. http://www.sciencedirect.com/science/article/B6V2R-48KF7Y8-1/2/3ebd02d524ce26db2ca47735385023d910.1016/S0013-7944(03)00133-4 ↗
43. Scheider I, Brocks W (2006) Cohesive elements for thin-walled structures. Computational Mater Sci 37(12): 101–109. doi: 10.1016/j.commatsci.2005.12.04210.1016/j.commatsci.2005.12.042 ↗
44. Scheyvaerts F, Onck P, Tekoglu C, Pardoen T (2011) The growth and coalescence of ellipsoidal voids in plane strain under combined shear and tension. J Mech Phys Solids 59(2): 373–397. doi: 10.1016/j.jmps.2010.10.00310.1016/j.jmps.2010.10.003 ↗
45. Simo J, Kennedy J (1992) On a stress resultant geometrically exact shell model. Part V. Nonlinear plasticity: formulation and integration algorithms. Comput Methods Appl Mech Eng 96(2):133–171. doi: 10.1016/0045-7825(92)90129-8 . http://www.sciencedirect.com/science/article/B6V29-47YJHG3-T/2/9de358cec2b4c5890934d756457471dc10.1016/0045-7825(92)90129-8 ↗
46. Simo JC, Fox DD (1989) On stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization. Comput Methods Appl Mech Eng 72(3): 267–30410.1016/0045-7825(89)90002-9 ↗
47. Simo JC, Fox DD, Rifai MS (1989) On a stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects. Comput Methods Appl Mech Eng 73(1): 53–9210.1016/0045-7825(89)90098-4 ↗
48. Simo J, Fox D, Rifai M (1990a) On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory. Comput Methods Appl Mech Eng 79(1):21–70. doi: 10.1016/0045-7825(90)90094-3 . http://www.sciencedirect.com/science/article/B6V29-47XSWMP-3/2/a7d8adf2ee1bde1ca1943b2179e27a9a10.1016/0045-7825(90)90094-3 ↗
49. Simo JC, Rifai MS, Fox DD (1990b) On a stress resultant geometrically exact shell model. Part IV: variable thickness shells with through-the-thickness stretching. Comput Methods Appl Mech Eng 81(1):91–126. doi: 10.1016/0045-7825(90)90143-A . http://www.sciencedirect.com/science/article/B6V29-4808WRV-30/2/57f79632994b5829488baed916c1a99810.1016/0045-7825(90)90143-A ↗
50. Süli E, Mozolevski I (2007) hp-version interior penalty dgfems for the biharmonic equation. Comput Methods Appl Mech Eng 196(1316): 1851–1863. doi: 10.1016/j.cma.2006.06.01410.1016/j.cma.2006.06.014 ↗
51. Tvergaard V (1990) Effect of fibre debonding in a whisker-reinforced metal. Mater Sci Eng A 125(2): 203–213. doi: 10.1016/0921-5093(90)90170-810.1016/0921-5093(90)90170-8 ↗
52. Tvergaard V, Hutchinson JW (1992) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J Mech Phys Solids 40(6): 1377–1397. doi: 10.1016/0022-5096(92)90020-310.1016/0022-5096(92)90020-3 ↗
53. Tvergaard V, Hutchinson JW (1993) The influence of plasticity on mixed mode interface toughness. J Mech Phys Solids 41(6): 1119–1135. doi: 10.1016/0022-5096(93)90057-M10.1016/0022-5096(93)90057-M ↗
54. Tvergaard V, Hutchinson JW (1996) Effect of strain-dependent cohesive zone model on predictions of crack growth resistance. Int J Solids Struct 33(20–22):3297–3308. http://www.sciencedirect.com/science/article/B6VJS-3VTSPVJ-S/2/71976b9761cf9bd81d308e234b91cf3b10.1016/0020-7683(95)00261-8 ↗
55. Weibull W (1939) A statistical theory of strength of materials. In: Proceedings of the Ingeniors Vetenskapsakad, p 151
56. Wells GN, Dung NT (2007) A c0 discontinuous galerkin formulation for kirchhoff plates. Comput Methods Appl Mech Eng 196(35–36): 3370–338010.1016/j.cma.2007.03.008 ↗
57. Wyart E, Coulon D, Duflot M, Pardoen T, Remacle JF, Lani F (2007) A substructured fe-shell/xfe-3d method for crack analysis in thin-walled structures. Int J Numer Methods Eng 72(7): 757–779. doi: 10.1002/nme.202910.1002/nme.2029 ↗
58. Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42(9): 1397–1434. doi: 10.1016/0022-5096(94)90003-510.1016/0022-5096(94)90003-5 ↗
59. Zavattieri P (2004) Modeling of crack propagation in thin-walled structures. Mecanica Comput XXIII:209–228
60. Zavattieri PD (2006) Modeling of crack propagation in thin-walled structures using a cohesive model for shell elements. J Appl Mech 73(6):948–958. http://link.aip.org/link/?AMJ/73/948/110.1115/1.2173286 ↗
61. Zhang ZJ, Paulino GH, Celes W (2007) Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials. Int J Numer Methods Eng 72(8): 893–923. doi: 10.1002/nme.203010.1002/nme.2030 ↗
62. Zhou F, Molinari JF (2004a) Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency. Int J Numer Methods Eng 59(1): 1–24. doi: 10.1002/nme.85710.1002/nme.857 ↗
63. Zhou F, Molinari JFc (2004) Stochastic fracture of ceramics under dynamic tensile loading. Int J Solids Struct 41(22–23): 6573–6596. doi: 10.1016/j.ijsolstr.2004.05.02910.1016/j.ijsolstr.2004.05.029 ↗