A finite element model for direction-dependent mechanical response to nanoindentation of cortical bone allowing for anisotropic post-yield behavior of the tissue

Journal of Biomechanical Engineering

Volumn 132, Issue 8, 2010, Pages

  Carnelli, D ^a,b   Gastaldi, D ^a   Sassi, V ^a   Contro, R ^a   Ortiz, C ^b   Vena, P ^a,c  

^a POLITECNICO DI MILANO   (Italy)

^b Massachusetts Institute of Technology Cambridge   (United States)

^c IRCCS ISTITUTO ORTOPEDICO GALEAZZI   (Italy)

Author keywords

Anisotropic yield function; Cortical bone; Finite element; Indentation

Indexed keywords

ANISOTROPIC ELASTIC; ANISOTROPIC MATERIAL; ANISOTROPIC YIELD FUNCTIONS; CONSTITUTIVE PARAMETERS; CORTICAL BONE; DEFORMATION MODES; ELASTIC PROPERTIES; EXPERIMENTAL DATA; EXPERIMENTAL STUDIES; FINITE ELEMENT; FINITE ELEMENT MODELS; HUMAN BONES; INDENTATION EXPERIMENT; INDENTATION MODULUS; INELASTIC STRAIN; ISOTROPIC SOLIDS; LINEAR TRANSFORMATION; LONG BONE; LONGITUDINAL DIRECTION; MATERIAL MODELS; MECHANICAL RESPONSE; MICRO-STRUCTURAL; NANOINDENTATION TESTS; NUMERICAL MODELS; NUMERICAL SIMULATION; PROBE TIPS; STRESS TENSORS; TENSION-COMPRESSION; TISSUE HARDNESS; TRANSVERSE DIRECTIONS; YIELD BEHAVIORS;

ANISOTROPY; BONE; COMPUTER SIMULATION; FINITE ELEMENT METHOD; HARDNESS; LINEAR TRANSFORMATIONS; NANOINDENTATION;

YIELD STRESS;

ANISOTROPY; ARTICLE; BONE DEFORMATION; CORTICAL BONE; ELASTICITY; FINITE ELEMENT ANALYSIS; HARDNESS; HUMAN; MECHANICAL STRESS; BIOLOGICAL MODEL; BONE; COMPUTER SIMULATION; METHODOLOGY; NANOTECHNOLOGY; PHYSIOLOGY; STIMULATION; VISCOSITY; YOUNG MODULUS;

ANISOTROPY; BONE AND BONES; COMPUTER SIMULATION; ELASTIC MODULUS; FINITE ELEMENT ANALYSIS; HARDNESS; HARDNESS TESTS; HUMANS; MODELS, BIOLOGICAL; NANOTECHNOLOGY; PHYSICAL STIMULATION; STRESS, MECHANICAL; VISCOSITY;

EID: 77955409703     PISSN: 01480731     EISSN: 15288951     Source Type: Journal    
DOI: 10.1115/1.4001358     Document Type: Article

References (43)

1. Rho, J., Roy, M., Tsui, T., and Pharr, G., 1999, "Elastic Properties of Microstructural Components of Human Bone Tissue as Measured by Nanoindentation," J. Biomed. Mater. Res., 45, pp. 48-54. (Pubitemid 29068438)
2. Ebenstein, D., and Pruitt, L., 2006, "Nanoindentation of Biological Materials," Nanotoday, 1, pp. 26-33.
3. Lewis, G., and Nyman, J., 2008, "Review, The Use of Nanoindentation for Characterizing the Properties of Mineralized Hard Tissues: State-of-the Art Review," J. Biomed. Mater. Res., Part B: Appl. Biomater., 87B, pp. 286-301.
4. Rho, J., Tsui, T. Y., and Pharr, G. M., 1997, "Elastic properties of Human Cortical and Trabecular Lamellar Bone Measured by Nanoindentation," Biomaterials, 18, pp. 1325-1330.
5. Rho, J., Zioupos, P., Currey, J. D., and Pharr, G. M., 2002, "Microstructural Elasticity and Regional Heterogeneity in Human Femoral Bone of Various Ages Examined by Nano-Indentation," J. Biomech., 35, pp. 189-198.
6. Wang, X., Chen, X., Hodgson, P., and Wen, C., 2006, "Elastic Modulus and Hardness of Cortical and Trabecular Bovine Bone Measured by Nanoindentation," Trans. Nonferrous Met. Soc. China, 16, pp. s744-s748. (Pubitemid 44171594)
7. Hansma, P., Turner, P., Fantner, G., 2006, "Bone Diagnostic Instrument," Rev. Sci. Instrum., 77, p. 075105.
8. Oliver, W., and Pharr, G., 1992, "An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments," J. Mater. Res., 7, pp. 1564-1583.
9. Currey, J., 2002, Bones: Structure and Mechanics, Princeton University Press, NJ.
10. Weiner, S., Addadi, L., and Wagner, H., 2000, "Materials Design in Biology," Mater. Sci. Eng., C, 11, pp. 1-8.
11. Lees, S., and Page, E., 1992, "A Study of Some Properties of Mineralized Turkey Leg Tendon," Connect. Tissue Res., 28, pp. 263-287.
12. Liu, D., Wagner, H., and Weiner, S., 2000, "Bending and Fracture of Compact Circumferential and Osteonal Lamellar Bone of the Baboon Tibia," J. Mater. Sci.: Mater. Med., 11, pp. 49-60.
13. Liu, D., Wagner, H., and Weiner, S., 1999, "Anisotropic Mechanical Properties of Lamellar Bone Using Miniature Cantilever Bending Specimens," J. Biomech., 32, pp. 647-654.
14. Fratzl, P., and Weinkamer, R., 2007, "Nature's Hierarchical Materials," Prog. Mater. Sci., 52(8), pp. 1263-1334.
15. Cowin, S., 1989, Bone Mechanics, CRC, Boca Raton, FL.
16. Mercer, C., He, R., Wang, M. Y., and Evans, A., 2006, "Mechanisms Governing the Inelastic Deformation of Cortical Bone and Application to Trabecular Bone," Acta Biomater., 2, pp. 59-68. (Pubitemid 43348745)
17. Mullins, L., Bruzzi, M., and McHugh, P., 2009, "Calibration of a Constitutive Model for the Post-Yield Behaviour of Cortical Bone," J. Mech. Behav. Biomed. Mater., 2, pp. 460-470.
18. Tai, K., Ulm, F., and Ortiz, C., 2006, "Nanogranular Origins of the Strength of Bone," Nano Lett., 6, pp. 2520-2525.
19. Tai, K., Dao, M., Suresh, S., Palazoglu, A., and Ortiz, C., 2007, "Nanoscale Heterogeneity Promotes Energy Dissipation in Bone," Nature Mater., 6, pp. 454-462.
20. Fan, Z., Rho, J., and Swadener, J., 2004, "Three-Dimensional Finite Element Analysis of the Effects of Anisotropy on Bone Mechanical Properties Measured by Nanoindentation," J. Mater. Res., 19, pp. 114-123.
21. Zhang, J., Niebur, G., and Ovaert, T., 2008, "Mechanical Property Determination of Bone Through Nano- and Micro-Indentation Testing and Finite Element Simulation," J. Biomech., 41, pp. 267-275.
22. Swadener, J., and Pharr, G., 2001, "Indentation of Elastically Anisotropic Half-Spaces by Cones and Parabolas of Revolution," Philos. Mag. A, 81, pp. 447-466. (Pubitemid 33581893)
23. Swadener, J., Rho, J., and Pharr, G., 2001, "Effects of Anisotropy on Elastic Moduli Measured by Nanoindentation in Human Tibial Cortical Bone," J. Biomed. Mater. Res. Part A, 57, pp. 108-112.
24. Zysset, P., and Curnier, A., 1995, "An alternative model for Anisotropic Elasticity Based on Fabric Tensors," Mech. Mater., 21, pp. 243-250.
25. Malvern, L., 1969, Introduction to the Mechanics of a Continous Medium, Prentice-Hall, Englewood Cliffs, NJ.
26. Car, E., Oller, S., and Oñate, E., 2000, "An Anisotropic Elastoplastic Constitutive Model for Large Strain Analysis of Fiber Reinforced Composite Materials," Comput. Methods Appl. Mech. Eng., 185, pp. 245-277.
27. Drucker, D., and Prager, W., 1952, "Soil Mechanics and Plastic Analysis or Limit Design," Q. Appl. Math., 10, pp. 157-165.
28. Meyers, M., Chen, P., Yu-Min Lin, A., and Seki, Y., 2008, "Biological Materials: Structure and Mechanical Properties," Prog. Mater. Sci., 53, pp. 1-206. (Pubitemid 350017839)
29. Zienkiewicz, O., and Taylor, R., 1991, The Finite Element Method, 4th ed., McGraw-Hill, England, Vol. 2.
30. ABAQUS, 2009, Documentation Manual, ABAQUS Simulia.
31. Bayraktar, H., Morgan, E., Niebur, G., Morris, G., Wong, E., and Keaveny, T., 2004, "Comparison of the Elastic and Yield Properties of Human Femoral Trabecular and Cortical Bone Tissue," J. Biomech., 37, pp. 27-35.
32. Reilly, D., and Burstein, A., 1975, "The Elastic and Ultimate Properties of Compact Bone Tissue," J. Biomech., 8, pp. 393-405.
33. Wang, L., Song, J., Ortiz, C., and Boyce, M., 2009, "Anisotropic Design of a Multilayered Biological Exoskeleton," J. Mater. Res., 24, pp. 3477-3494.
34. Dao, M., Chollacoop, N., Van Vliet, K., Venkatesh, T., and Suresh, S., 2001, "Computational Modeling of the Forward and Reverse Problems in Instrumented Sharp Indentation," Acta Mater., 49, pp. 3899-3918.
35. Qin, J., Huang, Y., Xiao, J., and Hwang, K., 2009, "The Equivalence of Axisymmetric Indentation Model for Three-Dimensional Indentation Hardness," J. Mater. Res., 24, pp. 776-783.
36. Bembey, A., Koonjul, V., Bushby, A., Ferguson, V., and Boyde, A., 2005, "Contribution of Collagen, Mineral and Water Phases to the Nanomechanical Properties of Bone," Material Research Society, Symposium Proceedings, Vol. 844.
37. Oyen, M., Ko, C., Bembey, A., Bushby, A., and Boyde, A., 2005, "Nanoindentation and Finite Element Analysis of Resin-Embedded Bone Samples as a Three-Phase Composite Material," Material Research Society Symposium, Vol. 874.
38. Akhtar, R., Morse, S., and Mummery, P., 2005, "Nanoindentation of Bone in a Physiological Environment," Materials Research Society Symposium Proceedings, Vol. 84, pp. 87-92.
39. Fan, Z., Swadener, J., Rho, J., Roy, M., Pharr, G., 2002, "Anisotropic Properties of Human Tibial Cortical Bone as Measured by Nanoindentation," J. Orthop. Res., 20, pp. 806-810. (Pubitemid 34823002)
40. Gupta, H., Wagermaier, W., Zickler, G., Raz-Ben Aroush, D., Funari, S., Roscheger, P., Wagner, H., and Fratzl, P., 2005, "Nanoscale Deformation Mechanisms in Bone," Nano Lett., 5, pp. 2108-2111.
41. Gupta, H., Seto, J., Wagermaler, W., Zaslansky, P., Boesecke, P., and Fratzl, P., 2006, "Cooperative Deformation of Mineral and Collagen in Bone at the Nanoscale," Proc. Natl. Acad. Sci. U.S.A., 103, pp. 17741-17746.
42. Gupta, H., Roschger, P., Wagner, H., and Fratzl, P., 2006, "Mechanical Modulation at the Lamellar Level in Osteonal Bone," J. Mater. Res., 21, pp. 1913-1921.
43. Peterlik, H., Roschger, P., Klaushofer, K., and Fratzl, P., 2006, "From Brittle to Ductile Fracture of Bone," Nature Mater., 5, pp. 52-55.