Achieving pervasive fracture and fragmentation in three-dimensions: an unstructuring-based approach
Source abstract
Abstract
There are few methods capable of capturing the full spectrum of pervasive fracture behavior in three-dimensions. Throughout pervasive fracture simulations, many cracks initiate, propagate, branch and coalesce simultaneously. Because of the cohesive element method framework, this behavior can be captured in a regularized manner. However, since the cohesive element method is only able to propagate cracks along element facets, a poorly designed discretization of the problem domain may introduce artifacts into the simulated results. To reduce the influence of the discretization, geometrically and constitutively unstructured means can be used. In this paper, we present and investigate the use of three-dimensional nodal perturbation to introduce geometric randomness into a finite element mesh. We also discuss the use of statistical methods for introducing randomness in heterogeneous constitutive relations. The geometrically unstructured method of nodal perturbation is then combined with a random heterogeneous constitutive relation in three numerical examples. The examples are chosen in order to represent some of the significant influencing factors on pervasive fracture and fragmentation; including surface features, loading conditions, and material gradation. Finally, some concluding remarks and potential extensions are discussed.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in engineering · Geophysical Methods and Applications · Rock Mechanics and Modeling
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (78)
Show source-provided references
1. ABAQUS, Version 6.11 Documentation (2011) Dassault Systemes Simulia Corp. Providence, RI, USA
2. Afferrante L, Ciavarella M, Valenza E (2006) Is Weibull’s modulus really a material constant? Example case with interacting collinear cracks. Int J Solids Struct 43:5147–515710.1016/j.ijsolstr.2005.08.002 ↗
3. Areias PMA, Belytschko T (2005) Analysis of three-dimensional crack initiation and propagation using the extended finite element method. Int J Numer Methods Eng 63:760–78810.1002/nme.1305 ↗
4. Atluri SN, Zhu T (1998) A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics. Comput Mech 22:117–12710.1007/s004660050346 ↗
5. Barenblatt GI (1959) The formation of equilibrium cracks during brittle fracture: general ideas and hypotheses. Axially symmetric cracks. J Appl Math Mech 23:255–265
6. Bathe K-J (1996) Finite element procedures. Prentice Hall, Upper Saddle River
7. Bažant ZP, Chen EP (1996) Scaling of structural failure. Technical Report, Sandia National Laboratories10.2172/420364 ↗
8. Bažant ZP, Luo W, Chau VT, Bessa MA (2016) Wave dispersion concepts of peridynamics compared to classical nonlocal damage models. J Appl Mech 83:111004-1–111004-410.1115/1.4034319 ↗
9. Becher PF, Sun EY, Plucknett KP, Alexander KB, Hsueh CH, Lin HT, Waters SB, Westmoreland CG (1998) Microstructural design of silicon nitride with improved fracture toughness: I effects of grain shape and size. J Am Ceram Soc 81:2821–283010.1111/j.1151-2916.1998.tb02702.x ↗
10. Belytschko T, Fleming M (1999) Smoothing, enrichment and contact in the element-free Galerkin method. Comput Struct 71:173–19510.1016/S0045-7949(98)00205-3 ↗
11. Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37:229–25610.1002/nme.1620370205 ↗
12. Belytschko T, Gu L, Lu YY (1994) Fracture and crack growth by element free Galerkin methods. Model Simul Mater Sci Eng 2:519–53410.1088/0965-0393/2/3A/007 ↗
13. Bishop JE (2009) Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations. Comput Mech 44:455–47110.1007/s00466-009-0383-6 ↗
14. Bishop JE, Strack OE (2011) A statistical method for verifying mesh convergence in Monte Carlo simulations with application to fragmentation. Int J Numer Meth Eng 88(3):279–30610.1002/nme.3176 ↗
15. Bishop J, Martinez MJ, Newell P (2016) Simulating fragmentation and fluid-induced fracture in disordered media using random finite-element meshes. Int J Multiscale Comput Eng 14(4):349–36610.1615/IntJMultCompEng.2016016908 ↗
16. Brannon R, Wells J, Erik Strack O (2007) Validating theories for brittle damage. Metall Mater Trans A 38:2861–286810.1007/s11661-007-9310-7 ↗
17. Caballero A, Molinari JF (2010) Finite element simulations of kidney stones fragmentation by direct impact: tool geometry and multiple impacts. Int J Eng Sci 48:253–26410.1016/j.ijengsci.2009.11.002 ↗
18. Caballero A, Molinari JF (2011) Optimum energy on the fragmentation of kidney stones by direct impact. Int J Comput-Aided Eng Softw 28:747–76410.1108/02644401111154655 ↗
19. Cavendish JC, Field DA, Frey WH (1985) An approach to automatic three-dimensional finite element mesh generation. Int J Numer Methods Eng 21:329–34710.1002/nme.1620210210 ↗
20. Celes W, Paulino GH, Espinha R (2005) A compact adjacency-based topological data structure for finite element mesh representation. Int J Numer Methods Eng 64:1529–155610.1002/nme.1440 ↗
21. Danzer R (1992) A general strength distribution function for brittle materials. J Eur Ceram Soc 10:461–47210.1016/0955-2219(92)90021-5 ↗
22. Delaunay B (1934) Sur la sphère vide. a la mémoire de Georges Voronoï, Bulletin de l’Académie des Sciences de l’URSS. Classe des sciences mathématiques et na 6:793–800
23. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–10410.1016/0022-5096(60)90013-2 ↗
24. Espinosa HD, Dwivedi S, Lu H-C (2000) Modeling impact induced delamination of woven fiber reinforced composites with contact/cohesive laws. Comput Methods Appl Mech Eng 183:259–29010.1016/S0045-7825(99)00222-4 ↗
25. Falk ML, Needleman A, Rice JR (2001) A critical evaluation of cohesive zone models of dynamic fracture. J Phys IV 11:43–50
26. Field DA (1988) Laplacian smoothing and Delaunay triangulations. Commun Appl Numer Methods 4:709–71210.1002/cnm.1630040603 ↗
27. Fischer RA, Tippett LHC (1928) Limiting forms of the frequency distribution of the largest and smallest member of a sample. Proc Camb Philos Soc 24:180–19010.1017/S0305004100015681 ↗
28. Fréchet M (1927) Sur la loi de probabilité de l’écart maximum. Annales de la Société de Mathématique 18:93–116
29. Freudenthal AM (1968) Statistical approach to brittle fracture, Ch. 6. Academic Press, New York, pp 591–616
30. Geuzaine C, Remacle J-F (2009) Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Meth Eng 79:1309–133110.1002/nme.2579 ↗
31. Hashimoto R, Ogawa A, Morimoto T, Yonaiyama M (1996) Spin test of silicon nitride disk. The 74th JSME Annual Meeting 2:441–442
32. Hinton E, Rock T, Zienkiewicz OC (1976) A note on mass lumping and related processes in the finite element method. Earthq Eng Struct Dyn 4:245–24910.1002/eqe.4290040305 ↗
33. Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis. Dover Publications, New York
34. Jayatilaka ADS, Trustrum K (1977) Statistical approach to brittle fracture. J Mater Sci 12:1426–143010.1007/BF00540858 ↗
35. Kallinderis Y, Vijayant P (1993) Adaptive refinement-coarsening scheme for three-dimensional unstructured meshes. Am Inst Aeronaut Astronaut J 31:1440–144710.2514/3.11793 ↗
36. Kim J-H, Paulino GH (2002) Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. ASME J Appl Mech 69:502–51410.1115/1.1467094 ↗
37. Klein PA, Foulk JW, Chen EP, Wimmer SA, Gao H (2000) Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods. Technical report, Sandia National Laboratories10.2172/772347 ↗
38. Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Math Comput 37:141–15810.1090/S0025-5718-1981-0616367-1 ↗
39. Levy S (2010) Exploring the physics behind dynamic fragmentation through parallel simulations. Ph.D. thesis, École Polytechnique Fédérale de Lausanne
40. Liu WK, Jun S, Zhang YF (1995) Reproducing kernel particle methods. Int J Numer Methods Fluids 20:1081–110610.1002/fld.1650200824 ↗
41. Lo SH (1991) Volume discretization into tetrahedra—II. 3D triangulation by advancing front approach. Comput Struct 39:501–51110.1016/0045-7949(91)90059-U ↗
42. Molinari JF, Ortiz M (2002) Three-dimensional adaptive meshing by subdivision and edge-collapse in finite-deformation dynamic-plasticity problems with application to adiabatic shear banding. Int J Numer Methods Eng 53:1101–112610.1002/nme.325 ↗
43. Mosler J, Ortiz M (2009) An error-estimate-free and remapping-free variational mesh refinement and coarsening method for dissipative solids at finite strains. Int J Numer Methods Eng 77:437–45010.1002/nme.2428 ↗
44. Mota A, Knap J, Ortiz M (2006) Three-dimensional fracture and fragmentation of artificial kidney stones. J Phys Conf Ser 46:299–30310.1088/1742-6596/46/1/041 ↗
45. Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element moethod: diffuse approximation and diffuse elements. Comput Mech 10:307–31810.1007/BF00364252 ↗
46. Newmark NM (1959) A method of computation for structural dynamics. J Eng Mech Div 85(7):67–9410.1061/JMCEA3.0000098 ↗
47. Nguyen VP, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: review and key computer implementation aspects. Math Comput Simul 79:763–81310.1016/j.matcom.2008.01.003 ↗
48. Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44:1267–128210.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7 ↗
49. Ostoja-Starzewski M, Wang G (2006) Particle modeling of random crack patterns in epoxy plates. Probab Eng Mech 21:267–27510.1016/j.probengmech.2005.10.007 ↗
50. Park K (2009) Potential-based fracture mechanics using cohesive zone and virtual internal bond modeling. Ph.D. thesis, University of Illinois at Urbana-Champaign
51. Park K, Paulino GH, Roesler JR (2009) A unified potential-based cohesive model for mixed-mode fracture. J Mech Phys Solids 57:891–90810.1016/j.jmps.2008.10.003 ↗
52. Park K, Paulino GH, Celes W, Espinha R (2012) Adaptive mesh refinement and coarsening for cohesive zone modeling of dynamic fracture. Int J Numer Methods Eng 92:1–3510.1002/nme.3163 ↗
53. Paulino GH, Celes W, Espinha R, Zhang ZJ (2008) A general topology-based framework for adaptive insertion of cohesive elements in finite element meshes. Eng Comput 24:59–7810.1007/s00366-007-0069-7 ↗
54. Paulino GH, Park K, Celes W, Espinha R (2010) Adaptive dynamic cohesive fracture simulations using nodal perturbation and edge-swap operators. Int J Numer Meth Eng 84:1303–134310.1002/nme.2943 ↗
55. Peirce FT (1926) Tensile tests for cotton yarns, part V: the weak wink wheorems on the strength of long and composite specimens. J Text Inst 17:355–36810.1080/19447027.1926.10599953 ↗
56. Pittomvils G, Vandeursen H, Wevers M, Lafaut JP, De Ridder D, De Meester P, Boving R, Baert L (1994) The influence of internal stone structure upon the fracture behavior of urinary calculi. Ultrasound Med Biol 20:803–81010.1016/0301-5629(94)90037-X ↗
57. Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61:2316–234310.1002/nme.1151 ↗
58. Santare MH, Lambros J (2000) Use of graded finite elements to model the behavior of nonhomogeneous materials. J Appl Mech 67:819–82210.1115/1.1328089 ↗
59. Schröberl J (1997) Netgen—an advancing front 2D/3D-mesh generator based on abstract rules. Comput Vis Sci 1:41–5210.1007/s007910050004 ↗
60. Schroeder WJ, Shephard MS (1988) Geometry-based fully automatic mesh generation and the Delaunay triangulation. Int J Numer Meth Eng 26:2503–251510.1002/nme.1620261109 ↗
61. Silling SA, Bobaru F (2005) Peridynamic modeling of membranes and fibers. Int J Nonlinear Mech 40:395–40910.1016/j.ijnonlinmec.2004.08.004 ↗
62. Simo JC, Wriggers P, Schweizerhof KH, Taylor RL (1986) Finite deformation post-buckling analysis involving inelasticity and contact constraints. Int J Numer Methods Eng 23:779–80010.1002/nme.1620230504 ↗
63. Song JH, Belytschko T (2009) Cracking node method for dynamic fracture with finite elements. Int J Numer Methods Eng 77:360–38510.1002/nme.2415 ↗
64. Spring DW, Giraldo-Londono O, Paulino GH (2016) A study on the thermodynamic consistency of the Park-Paulino-Roesler (PPR) cohesive fracture model. Mech Res Commun 78:100–10910.1016/j.mechrescom.2016.05.006 ↗
65. Sukumar N, Moes N, Moran B, Belytschko T (2000) Extended finite element method for three-dimensional crack modeling. Int J Numer Methods Eng 48:1549–157010.1002/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-A ↗
66. Sulsky D, Schreyer L (2004) MPM simulation of dynamic material failure with a decohesion constitutive model. Eur J Mech A Solids 23:423–44510.1016/j.euromechsol.2004.02.007 ↗
67. Sun EY, Becher PF, Plucknett KP, Hsueh CH, Alexander KB, Waters SB (1998) Microstructural design of silicon nitride with improved fracture toughness: II Effects of yttria and alumina additives. J Am Ceram Soc 81:2831–284010.1111/j.1151-2916.1998.tb02703.x ↗
68. Swank LR, Williams RM (1981) Correlation of static strengths and speeds of rotational failure of structural ceramics. Am Ceram Soc Bull 60:830–834
69. Vocialta M, Richart N, Molinari JF (2016) 3D dynmaic fragmentation with parallel dynamic insertion of cohesive elements. Int J Numer Meth Eng 109:1655–167810.1002/nme.5339 ↗
70. von Mises R (1936) La distribution de la plus grande de $$n$$ n valeurs. Rev Math Union Interbalcanique 1:141–160
71. Wang G, Al-Ostaz A, Cheng AH-D, Raju Mantena P (2008) Particle modeling of dynamic fracture simulation of a 2D polymeric material (nylon-6,6) subject to the impact of a rigid indenter. Comput Mater Sci 44:449–46310.1016/j.commatsci.2008.04.014 ↗
72. Weibull W (1939) A statistical theory of the strength of materials. Proc R Acad Eng Sci 151:1–45
73. Zhang Z (2003) Cohesive zone modeling of dynamic failure in homogeneous and functionally graded materials, Master’s thesis, University of Illinois at Urbana-Champaign
74. Zhang Z, Paulino GH (2005) Cohesive zone modeling of dynamic failure in homogeneous and functionally graded materials. Int J Plast 21:1195–125410.1016/j.ijplas.2004.06.009 ↗
75. Zhang Z, Paulino GH, Celes W (2007) Extrinsic cohesive zone modeling of dynamic fracture and microbranching instability in brittle materials. Int J Numer Methods Eng 72:893–92310.1002/nme.2030 ↗
76. Zhong P, Chuong CJ, Goolsby RD (1992) Microhardness measurements of renal calculi: regional differences and effects of microstructure. J Biomed Mater Res 26:1117–113010.1002/jbm.820260902 ↗
77. Zhong P, Chuong CJ, Preminger GM (1993) Characterization of fracture thoughness of renal calculi using a microindentation technique. J Mater Sci Lett 12:1460–146210.1007/BF00591608 ↗
78. Zhou F, Molinari JF (2004) Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency. Int J Numer Meth Eng 59:1–2410.1002/nme.857 ↗