Fracture strength assessment and aging signs detection in human cortical bone using an X-FEM multiple scale approach

Computational Mechanics

Volumn 42, Issue 4, 2008, Pages 579-591

  Budyn, Elisa ^a   Hoc, Thierry ^b   Jonvaux, Julien ^a  

^a 1120 Science and Engineering Offices   (United States)

^b ECOLE CENTRALE PARIS   (France)

Author keywords

Cortical bone; Failure; Multiple cracks; Multiple scale; X FEM

Indexed keywords

BONE; COMPUTER SYSTEM RECOVERY; CRACK PROPAGATION; CRACKS; FINITE ELEMENT METHOD; FRACTURE TOUGHNESS; MECHANICAL PROPERTIES; MICROSTRUCTURE; RISK ASSESSMENT; SOLVENTS;

CORTICAL BONE; CRITICAL STRESS INTENSITY FACTOR; EXTENDED FINITE ELEMENT METHOD; FRACTURE RISK ASSESSMENTS; MECHANICAL CHARACTERISTICS; MULTIPLE CRACK; MULTIPLE SCALE; MULTIPLE-SCALE APPROACH;

FRACTURE;

EID: 47249128556     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-008-0283-1     Document Type: Article

References (67)

1. Katz JL (1976) Hierarchical modeling of compact haversian bone as a fiber reinforced material. Adv Bioeng ASME 17-18
2. Aoubiza B, Crolet JM, Meunier A (1996) On the mechanical characterization of compact bone structure using the homogenization theory. J Biomech 29(12): 1539-1547
3. Gottesman G, Hashin Z (1980) Analysis of viscoelastic behaviour of bones on the basis of microstructure. J Biomech 13: 89-96
4. Hogan HA (1992) Micromechanics modeling of haversian cortical bone properties. J Biomech 25(5): 549-556
5. Currey JD (2003) The many adaptations of bone. J Biomech 36: 1485-1495
6. Wright TM, Hayes WC (1977) Fracture mechanics parameters for compact bone-effects of density and specimen thickness. J Biomech 10: 419-430
7. Hui SL, Slemenda CM, Johnston CC (1988) Age and bone mass as predictors of fracture in a prospective study. J Clin Invest 81: 1804-1809
8. Schaffler MB, Burr DB (1988) Stiffness of compact bone effect of porosity and density. J Biomech 21: 13-16
9. O'Brien FJ, Taylor D, Lee TC (2005) The effect of bone microstructure on the initiation and growth of microcracks. J Orthop Res 23: 475-480
10. Mohsin S, O'Brien FJ, Lee TC (2006) Osteonal crack barriers in ovine compact bone. J Anat 208: 81-89
11. Nalla RK, Kinney JH, Ritchie RO (2003) Mechanistic fracture criteria for the failure of human cortical bone. Nat Mater 2: 164-168
12. Katz JL (1971) Hard tissue as composite material-i. Bounds on the elastic behavior. J Biomech 4(5): 455-473
13. Dong XN, Zhong XN, Huang YY, Guo XE (2005) A generalized self-consisitent estimate for the effective elastic moduli for fiber-reinforced composite materials with multiple transversely isotropic inclusions. Int J Mech Sci 47(6): 922-940
14. Dong XN, Guo XE (2006) Prediction of cortical bone elastic constants by a two-level micromechanical model using a generalized self-consistent method. J Biomech Eng Trans ASME 128(3): 309-316
15. Prendergast PJ, Huiskes R (1996) Microdamage and osteocyte-lacuna strain in bone: a microstructural finite element analysis. J Biomech Eng Trans ASME 118: 240-246
16. Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5): 610-620
17. Belytschko T, Moës N, Usui S, Parimi C (2001) Arbitrary discontinuities in finite elements. Int J Numer Methods Eng 50(4): 993-1013
18. Melenk JM, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 39: 289-314
19. Dolbow J, Moës N, Belytschko T (2001) An extended finite element method for modeling crack growth with frictional contact. Comput Methods Appl Mech Eng 190(51-52): 6825-6846
20. Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1): 131-150
21. Budyn E, Zi G, Moës N, Belytschko T (2004) A method for multiple crack growth in brittle materials without remeshing. Int J Numer Methods Eng 61(10): 1741-1770
22. Budyn E, Hoc T (2007) Multiple scale modeling of cortical bone fracture in tension using X-FEM. Revue Européenne de Mécanique Numrique (Eur J Comput Mech) 16: 213-236
23. Osher S, Sethian JA (1988) Fronts propagating with curvature dependent speed: algorithms based on hamilton-jacobi formulations. J Comput Phys 79(1): 12-49
24. Sethian JA (1999) Level sets methods & fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision and materials science. Cambridge University Press, Cambridge
25. Burchard P, Cheng LT, Merriman B, Osher S (2001) Rmotion of curves in three spacial dimensions using a level set approach. Int J Numer Methods Fluids 170: 720-741
26. Osher S, Cheng LT, Kang M, Shim Y, Tsai YH (2002) Geometricoptics in a phase-space-based level set and eulerian framework. J Comput Phys 179(2): 622-648
27. Ventura G, Budyn E, Belytschko T (2003) Meshfree and particle methods and their applications. Int J Numer Methods Eng 58: 1571-1792
28. Moran B, Shih CF (1987) A general treatment of crack tip contour integrals. Int J Fract 35: 295-310
29. Torquato S (2000) Random heterogeneous media-microstructure and macroscopic properties-interdisciplinary applied mathematics-mechanics and materials. Springer, New York
30. ABAQUS (2004) User's manual. Hibbit, Version 6.3, Karlsson & Sorensen, Providence
31. MATLAB7 (2006) User's manual. MATLAB, Version 7, The MathWorks, USA
32. GMSH (2006) User's manual. GMSH, Version 62, Geuzaine & Remacle, Cleveland USA; Louvain Belgium
33. Fan Z, Swadener E, Rho JY, Roy ME, Pharr GM (2002) Anisotropic properties of human tibial cortical bone as measured by nanoindentation. J Orthop Res 20: 806-810
34. Hoc T, Henry L, Verdier M, Aubry D, Sedel L, Meunier A (2006) Effect of microstructure on the mechanical properties of haversian cortical bone. Bone 38: 466-474
35. Henry L, Hoc T, Budyn E (2007) Microextensometry and mechanical behaviour of haversian cortical bone. Eur J Comput Mech (submitted)
36. Reilly DT, Burstein AH (1975) The elastic and ultimate properties of compact bone tissue. J Biomech 8(6): 393-405
37. Katz JL, Ukraincik K (1971) On the anisotropic elastic properties of hydroxyapatite. J Biomech 29(4): 221-227
38. Shelton DR, Martin RB, Stover SM, Gibeling JC (2003) Transverse fatigue crack propagation behavior in equine cortical bone. J Mater Sci 38: 3501-3508
39. Hazenberg JG, Taylor D, Lee TC (2006) Mechanisms of short crack growth at constant stress in bone. Biomaterials 27: 2114-2122
40. Lakes R, Saha S (1979) Cement line motion in bone. Nature 204: 501-503
41. Sabelman EE, Koran P, Diep N, Lineaweaver WC (1997) Collagen/hyaluronic acid matrices for connective tissue repair. In: First Smith & Nephew international symposium: advances in tissues engineering and biomaterials
42. Sumner DR (2006) Private communications
43. Rho JY, Zioupos P, Currey JD, Pharr GM (2002) Microstructural elasticity and regional heterogeneity in human femoral bone of various ages examined by nano-indentation. J Biomech 35: 189-198
44. Pattin CA, Calet WE, Carter DR (1996) Cyclic mechanical property degradation during fatigue loading of cortical bone. J Biomech 29: 69-79
45. Bayraktar HH, Morgan EF, Niebur GL, Morris GE, Wong EK, Keaveny TM (2004) Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J Biomech 37: 27-35
46. Budyn E, Hoc T (2006) Multiple scale modeling for crack growth in cortical bone under tension using the extended finite element method. Revue Européenne de Mécanique Numérique (Eur J Finite Element Methods), Special Issue (submitted)
47. Paris PC, Sih SC (1965) Stress analysis of cracks. In: Fracture toughness and testing and its applications. Society for Testing and Materials, Philadelphia, pp 30-83
48. Yau Y, Wang S, Corten H (1980) A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech 47: 335-341
49. Bocca P, Carpinteri A, Valente S (1991) Mixed mode fracture of concrete. Int J Solids Struct 27: 1139-1153
50. Nguyen QS, Stolz S (1985) ENDOMAGEMENT, FATIGUE, RUPTUE.-sur le problème en vitesse de propagation de fissure et de déplacement en rupture fragile ou ductile. note de nguyen quoc son et claude stolz, présentée par paul germain. Comptes- Rendus de l'Académie des Sciences de Paris, t. 301, Série II(10): 661-664
51. Nguyen QS, Stolz C, Debruyne G (1990) Energy methods in fracture mechanics: stability, bifurcation and second variations. Eur J Mech A/Solids 2: 157-173
52. Suo XZ, Combescure A (1989) Sur une formulation mathématique de la dérivée seconde de l'énergie potentielle en théorie de la rupture fragile. Comptes-Rendus de l'Académie des Sciences de Paris, t. 308, Série II:1119-1122
53. Suo XZ, Combescure A (1992) Double virtual crack extension method for crack growth stability assessment. Int J Fract 57: 127-150
54. Suo XZ, Valeta MP (1998) Second variation of energy and an associated line independent integral in fracture mechanics. ii numerical validations. Eur J Mech A/Solids 17(4): 541-565
55. Stazi FL, Budyn E, Chessa J, Belytschko T (2002) An extended finite element method with higher-order elements for curved cracks. Comput Mech 31: 38-48
56. Chessa J, Wang HW, Belytschko T (2003) On construction of blending elements for local partition of unity enriched finite elements. Int J Numer Methods Eng 57: 1015-1038
57. Kienzler R, Herrmann G (2002) Fracture criteria based on local propertiesof the eshelby tensor. Mech Res Commun 29(6): 521-527
58. Rubinstein A (1996) Macrocrack-microdefect interaction. J Appl Mech 53: 505-510
59. Demir I, Zbib HM, Khaleel M (2001) Microscopic analysis of crack propagation for multiple cracks, inclusions and voids. Theor Appl Fract Mech 36: 147-164
60. Deng H, Nemat-Nasser S (1992) Bridging multi-scale method for localization problems. Mech Mater 13: 15-36
61. Nemat-Nasser S, Hori M (1987) Toughening by partial or full bridging of cracks in ceramics and fiber reinforced composites. Mech Mater 6: 245-269
62. Jones AC, Sheppard AP, Sok RM, Arns CH, Limaye A, Averdunk H, Brandwood A, Sakellariou A, Senden TJ, Milthorpe BK, Knackstedt MA (2004) Three-dimensional analysis of cortical bone structure using X-ray micro-computed tomography. Phys A 339: 125-130
63. Qiu S, Rao DS, Fyhrie DP, Palnitkar S, Parfitt AM (2005) The morphological association between microcracks and osteocyte lacunae in human cortical bone. Bone 37: 10-15
64. Bloebaum RD, Liau DW, Lester DK, Rosenbaum TG (2006) Dual-energy x-ray absorptiometry measurement and accuracy of bone mineral after unilateral total hip arthroplasty. J Arthroplasty 21(4): 612-622
65. Cooper D, Turinsky A, Sensen C, Hallgrimsson B (2007) Effect of voxel size on 3d micro-ct analysis of cortical bone porosity. Calcif Tissue Int 80: 211-219
66. Advani SH, Lee TS, Martin RB (1987) Analysis of crack arrest by cement lines in osteonal bone. In: Proceedings of ASME Annu Winter Meeting, vol 3, pp 57-581
67. Guo XE, He MY, Goldstein SA (1995) Analysis of viscoelastic behaviour of bones on the basis of microstructure. Bioeng Conf ASME, BED- 29: 112-117