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Solid modeling aspects of three-dimensional fragmentation

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Abstract

The ways in which the topology and geometry of a three-dimensional finite-element model may evolve as a consequence of fracture and fragmentation are enumerated, and the actions which may be taken in order to update the boundary representation of the solid so as to faithfully reflect that evolution are described. Arbitrary topological and geometrical evolution of a three-dimensional solid, not necessarily restricted to an evolution of its surface, are addressed. Solids are described by their boundary representation (BRep) and a surface and volume triangulation. Fracture processes are modeled by the introduction of cohesive elements at element interfaces. Simple rules are shown to enable the simulation of strikingly complex crack patterns. The scope and versatility of the approach is illustrated with the aid of selected examples of application.

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References

  1. Requicha, A. A. G. (1980) Representations for rigid solids: theory, methods and systems, Computing Surveys, 12: 437–465

    Google Scholar 

  2. Mantyla, M. (1988) An Introduction to Solid Modeling, Computer Science Press, Rockwille, MD

    Google Scholar 

  3. Hoffmann, C. M. (1989) Geometric and Solid Modeling, Morgan Kaufmann, San Mateo, CA

    Google Scholar 

  4. Boender, E. Bronsvoort, W. F.; Post, F. H. (1994) Finite element mesh generation from constructive solid geometry models, Computer Aided Design, 26(5); 379–392

    Google Scholar 

  5. Rypl, D.; Krysl, P. (1997) Triangulation of 3d surfaces, Engineering with Computers, 13(2); 87–98

    Google Scholar 

  6. Camacho, G. T.; Ortiz, M. (1997) Adaptive Lagrangian modelling of ballistic penetration of metallic targets, Computer Methods in Applied Mechanics and Engineering, 142: 269–301

    Google Scholar 

  7. Radovitzky, R.; Ortiz, M. (1998) Tetrahedral mesh generation based on hole insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation, submitted

  8. Dyn, N.; Levin, D. (1990) A butterfly subdivision scheme for surface interpolation with tension control, AMC Transaction on Graphics, 9; 160–169

    Google Scholar 

  9. Dyn, N.; Levin, D.; Liu, D. (1992) Interpolatory convexity-preserving subdivision schemes for curves and surfaces, Computer-Aided Design, 24; 211–216

    Google Scholar 

  10. Kobbelt, L. (1996) Interpolatory subdivision on open quadrilateral nets with arbitrary topology, Computer Graphics Forum, 15(3), C409

    Google Scholar 

  11. Peraire, J.; Vahdati, M.; Morgan, K.; Zienkiewicz, O. C. (1987) Adaptive remeshing for compressible flow computations, Journal of Computational Physics, 72; 449–466

    Google Scholar 

  12. Peraire, J.; Peiro, J.; Formaggia, L.; Morgan, K.; Zienkiewicz, O. C. (1988) Finite element Euler computations in three dimensions, International Journal for Numerical Methods in Engineering, 26; 2135–2159

    Google Scholar 

  13. Lohner, R.; Parikh, P. (1988) Generation of three-dimensional unstructure grids by the advancing-front method, International Journal for Numerical Methods in Fluids, 8: 1135–1149

    Google Scholar 

  14. Morgan, K.; Peraire, J.; Peiro, J. (1991) The computation of three-dimensional flows using unstructured grids, Computer Methods in Applied Mechanics and Engineering, 87; 335–352

    Google Scholar 

  15. Peraire, J.; Peiro, J. (1992) Adaptive remeshing for three-dimensional compressible flow computations, Journal of Computational Physics, 103; 269–285

    Google Scholar 

  16. Probert, E. J.; Hassan, O.; Morgan, K.; Peraire, J. (1996) Unstructured tetrahedral mesh generation for three-dimensional viscous flows, International Journal for Numerical Methods in Engineering, 39; 549–567

    Google Scholar 

  17. Chan, C. T.; Anastasiou, K. (1997) An automatic tetrahedral mesh generation scheme by the advancingfront method, Communications in Applied Numerical Methods, 13; 33–46

    Google Scholar 

  18. Cavendish, J. C.; Field, D. A.; Frey, W. H. (1985) An approach to automatic three-dimensional finite element mesh generation, International Journal for Numerical Methods in Engineering, 21; 329–347

    Google Scholar 

  19. Marcum, D. L.; Weatherill, N. P. (1995) Unstructured grid generation using iterative point insertion and local reconnection, AIAA Journal, 33(9); 1619–1625

    Google Scholar 

  20. Schroeler, W. J.; Shephard, M. S. (1988) Geometrybased fully automatic mesh generation and the Delaunay triangulation, International Journal for Numerical Methods in Engineering, 26; 2503–2515

    Google Scholar 

  21. Baker, T. J. (1989) Automatic mesh generation for complex 3-dimensional regions using a constrained Delaunay triangulation, Engineering with Computers, 5; 161–175

    Google Scholar 

  22. Schroeder, W. J.; Shephard, M. S. (1989) AnO(N) algorithm to automatically generate geometric triangulation satisfying the Delaunay circumsphere criteria, Engineering with Computers, 5; 177–193

    Google Scholar 

  23. Weatherill, N. P. (1990) The integrity of geometrical boundaries in the two-dimensional Delaunay triangulation, Communications in Applied Numerical Methods, 6; 101–109

    Google Scholar 

  24. Schroeder, W. J.; Shephard, M. S. (1990) A combined octree/Delaunay method for fully automatic 3-d mesh generation, International Journal for Numerical Methods in Engineering, 29; 37–55

    Google Scholar 

  25. De Floriani, L.; Puppo, E. (1992) An on-line algorithm for constrained Delaunnay triangulation, CVGIP: Graphical Models and Image Processing, 54(3); 290–300

    Google Scholar 

  26. Sloan, S. W. (1993) A fast algorithm for generating constrained Delaunay triangulations, Computers and Structures, 47; 441–450

    Google Scholar 

  27. Muller, J. D.; Roe, P. L.; Deconinck, H. (1993) A frontal approach for internal node generation in Delaunay triangulations, International Journal for Numerical Methods in Fluids, 17; 241–255

    Google Scholar 

  28. Mavriplis, D. J. (1993) An advancing-front Delaunay triangulation algorithm designed for robustness, AIAA, paper 93-0671

  29. Weatherill, N. P.; Hassan, O. (1994) Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints, International Journal for Numerical Methods in Engineering, 37; 2005–2039

    Google Scholar 

  30. Wright, J. P.; Jack, A. G. (1994) Aspects of three-dimensional constrained Delaunay meshing, International journal for Numerical Methods in Engineering, 37 1841–1861

    Google Scholar 

  31. Borouchaki, H.; George, P. L.; Lo, S. H. (1996) Optimal Delaunay point insertion International Journal for Numerical Methods in Engineering, 39(20); 3407–3437

    Google Scholar 

  32. Fleischmann, P.; Selberherr, S. (1997) Three-dimensional Delaunay mesh generator using a modified advancing front approach. Proceedings of the 6th International meshing roundtable, 267–276, Park City, UT, Sandia National Laboratories

    Google Scholar 

  33. Shephard, M. S. (1985) Finite element modeling within an integrated geometric modeling environment: Part I-mesh generation, Engineering with Computers, 1; 61–71

    Google Scholar 

  34. Yerry, M. A.; Shephard, M. S. (1985) Automatic mesh generation for three-dimensional solids, Computers and Structures, 20; 211–223

    Google Scholar 

  35. Baehmann, P. L.; Wittchen, S. L.; Shephard, M. S.; Grice, K. R.; Yerry, M. A. (1987) Robust, geometrically based, automatic two-dimensional mesh generation, International Journal for Numerical Methods in Engineering, 24; 1043–1078

    Google Scholar 

  36. Baehmann, P. L.; Shephard, M. S.; Ashley, R. A.; Jay, A. (1988) Automated metalforming modeling utilizing adaptive remeshing and evolving geometry, Computers and Structures, 30; 319–325

    Google Scholar 

  37. Baehmann, P. L.; Shephard, M. S. (1989) Adaptive multiple-levelh-refinement in automated finite element analyses, Engineering with Computers, 5; 235–247

    Google Scholar 

  38. Shephard, M. S.; Georges, M. K. (1991) Automatic three-dimensional mesh generation by the finite octree technique, International Journal for Numerical Methods in Engineering, 32(4); 709–749

    Google Scholar 

  39. Brasher, D. G.; Butler, D. J. (1995) Explosive welding-principles and potentials, Advances in Materials Processing,147(3); 37–38

    Google Scholar 

  40. Goh, G. K. L.; Lim, L. C.; Rahman, M.; Lim, S. C. (1996) Transitions in wear mechanisms of alumina cutting tools, Wear, 201(1–2); 199–208

    Google Scholar 

  41. Ramanujachar, K.; Subramanian, S. V. (1996) Micromechanisms of tool wear in machining free cutting steels, Wear, 197(1–2); 45–55

    Google Scholar 

  42. Camacho, G. T.; Ortiz, M. (1996) Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures, 33(20–22); 2899–2938

    Google Scholar 

  43. Ortiz, M. (1996) Computational micromechanics, Computational Mechanics, 18; 321–338

    Google Scholar 

  44. Field, J. E. Sun, Q.; Townsend, D. (1989) Ballistic impact of ceramics. Inst. Phys. Conf. Ser. No. 102: Session 7, Paper presented at Int. Conf. Mech. Prop. Materials at High Rates of Strain, Oxford

  45. Kipp, M. E.; Grady, D. E.; Swegle, J.W. (1993) Numerical and experimental studies of high-velocity impact fragmentation, International Journal of Impact Engineering, 14; 427–438

    Google Scholar 

  46. Woodward, R. L.; Gooch, W. A.; O'Donnell, R. G.; Perciballi, W. J.; Baxter, B. J.; Pattie, S. D. (1994) A study of fragmentation in the ballistic impact of ceramics, International Journal of Impact Engineering, 15(5); 605–618

    Google Scholar 

  47. Piekutowski, A. J. (1995) Fragmentation of a sphere initiated by hypervelocity impact with a thin sheet, International Journal of Impact Engineering, 17; 627–638

    Google Scholar 

  48. Ortiz, M.; Suresh, S. (1993) Statistical properties of residual stresses and intergranular fracture in ceramic materials, Journal of applied Mechanics, 60; 77–84

    Google Scholar 

  49. Xu X. P.; Needleman, A. (1994) Numerical simulations of fast crack growth in brittle solids, Journal of the Mechanics and Physics of Solids, 42; 1397

    Google Scholar 

  50. De-Andrés, A.; Pérez, J. L.; Ortiz, M. (1998) Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. IJSS (in press)

  51. Potapov, A.; Campbell, C. S. (1996) A hybrid finite-element simulation of solid fracture, International Journal of Modern Physics, C 7(2); 155–180

    Google Scholar 

  52. Potapov, A.; Campbell, C. S. (1996) A three-dimensional simulation of brittle solid fracture, International Journal of Modern Physics, C, 7(5); 717–729

    Google Scholar 

  53. Rice, D. L.; Ting, E. C. (1993) Fragmentation algorithm for finite element failure simulation and analysis, International Journal for Numerical Methods in Engineering, 36; 3859–3881

    Google Scholar 

  54. Wawrzynek, P. A.; Martha, L. F.; Ingraffea, A. R. (1988) A computational environment for the simulation of fracture processes in three dimensions, analytical, numerical and experimental aspects of three dimensional fracture processes, ASME-AMD, 91; 321–327

    Google Scholar 

  55. Wawrzynek P. A.; Martha, L. F.; Ingraffea, A. R. (1989) Fransys: a software system for the simulation of crack propagation in three dimensions, Proc. Of the IUTAM/IACM Symposium on Discretization Methods in Structural Mechanics, Vienma, Austria, 271–282, July

  56. Martha, L. F.; Wawrzynek, P. A.; Ingraffea, A. R. (1990) Simulation of arbitrary crack propagation in three dimensions. In: A. R. Luxmore and D. R. J. Owen (eds), Numerical Methods in Fracture Mechanics-Proceedings of the Fifth International Conference Freiburg, Germany, 115–127, Pineridge Press

  57. Martha, L. F.; Wawrzynek, P. A.; Ingraffea, R. (1993) Arbitrary crack representation using solid modeling, Engineering and Computers, 9; 63–82

    Google Scholar 

  58. Ortiz, M.; Pandolfi, A. (1997) A class of cohesive elements for the simulation of three-dimensional crack propagation, IJNME (in press)

  59. Standish, T. A. (1995) Data Structures, Algorithms and Software Principles in C, Addison-Wesley, New York

    Google Scholar 

  60. Guillemin, V.; Pollack, A. (1974) Differential Topology, Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  61. Radovitzky, R.; Ortiz, M. (1997) Error estimation and adaptive meshing in strongly non-linear dynamic problems, Computer Methods in Applied Mechanics and Engineering (in press)

  62. Samet, H. (1990) The Design and Analysis of Spatial Data Structures, Addison-Wesley, New York

    Google Scholar 

  63. Mathur, K. K.; Needleman, A.; Tvergaard, V. (1996) Three dimensional analysis of dynamic ductile crack growth in a thin plate, Journal of the Mechanics and Physics of Solids, 44; 439–464

    Google Scholar 

  64. Dugdale, D. S. (1960) Yielding of steel sheets containingslits, Journal of the Mechanics and Physics of Solids, 8; 100–104

    Google Scholar 

  65. Willam, K. (1989) Simulation issues of distributed and localized failure computations. In: J. Mazars and Z. P. Bazant (eds), Cracking and Damage, 363–378, Elsevier Science, New York

    Google Scholar 

  66. Willam, K. (1989) Simulation issues of distributed and localized failure computations. In: J. Mazars and Z. P. Bazant (eds), Cracking and Damage, 363–378, Elsevier Science, New York

    Google Scholar 

  67. Xu, X.-P.; Needleman, A. (1995) Numerical simulations of dynamic interfacial crack growth allowing for crack growth away from the bond line, International Journal of Fracture, 74; 253–275

    Google Scholar 

  68. Xu, X.-P.; Needleman, A. (1996) Numerical simulations of dynamic crack growth along an interface, International Journal of Fracture, 74; 289–324

    Google Scholar 

  69. Belytschko, T. (1983) An overview of semidiscretization and time integration procedures. In: T. Belytschko and T. J. R. Hughes (eds), Computational Methods for Transient Analysis, 1–65, North-Holland

  70. Hughes, T. J. R. (1983) Analysis of transient algorithms with particular reference to stability behavior. In: T. Belytschko and T. J. R. Hughes (eds), Computational Methods for Transient Analysis, 67–155, North-Holland

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Authors and Affiliations

  1. Dipartimento di Ingegneria Strutturale, Politecnico di Milano, Milano, Italy

    A. Pandolfi

  2. Graduate Aeronautical Laboratories, California Institute of Technology, Mail Stop 105-50, 91125, Pasadena, CA, USA

    M. Ortiz

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  1. A. Pandolfi
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  2. M. Ortiz
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Pandolfi, A., Ortiz, M. Solid modeling aspects of three-dimensional fragmentation. Engineering with Computers 14, 287–308 (1998). https://doi.org/10.1007/BF01201761

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