Role of damage mechanics in nanoindentation of lamellar bone at multiple sizes: Experiments and numerical modeling

Journal of the Mechanical Behavior of Biomedical Materials

Volumn 4, Issue 8, 2011, Pages 1852-1863

  Lucchini, Riccardo ^a   Carnelli, Davide ^a,b   Ponzoni, Matteo ^a   Bertarelli, Emanuele ^a,c   Gastaldi, Dario ^a   Vena, Pasquale ^a,c  

^a POLITECNICO DI MILANO   (Italy)

^b EPFL   (Switzerland)

^c IRCCS ISTITUTO ORTOPEDICO GALEAZZI   (Italy)

Author keywords

Anisotropy; Damage mechanics; Finite element models; Lamellar bone; Nanoindentation

Indexed keywords

AXIAL DIRECTION; AXIAL INDENTATION; BONE MECHANICAL PROPERTIES; CONSTITUTIVE PARAMETERS; CONTACT STIFFNESS; CONTINUUM DAMAGE MODEL; CORTICAL BONE; DAMAGE MECHANICS; DAMAGE MECHANISM; FINITE ELEMENT MODELS; FORCE-DISPLACEMENT; INDENTATION CURVE; INDENTATION DEPTH; INDENTATION EXPERIMENT; INDENTATION MODULUS; MULTIPLE SCALE; NANOINDENTATION TESTS; NUMERICAL MODELING; NUMERICAL MODELS; QUANTITATIVE AGREEMENT; STIFFNESS LOSS; TRANSVERSE DIRECTIONS;

ANISOTROPY; BONE; DEGREES OF FREEDOM (MECHANICS); EXPERIMENTS; FINITE ELEMENT METHOD; MECHANICS; MECHANISMS; NUMERICAL METHODS; STIFFNESS; UNLOADING;

NANOINDENTATION;

ARTICLE; BIOMECHANICS; BONE STRUCTURE; CORTICAL BONE; DAMAGE MECHANICS; FINITE ELEMENT ANALYSIS; HARDNESS; LAMELLAR BONE; NANOINDENTATION; NONHUMAN; PRIORITY JOURNAL; QUANTITATIVE STUDY; RIGIDITY; SIMULATION; VALIDATION PROCESS;

ANIMALS; BIOMECHANICS; CATTLE; ELASTICITY; FINITE ELEMENT ANALYSIS; HARDNESS TESTS; NANOTECHNOLOGY; TIBIA;

EID: 81255158980     PISSN: 17516161     EISSN: 18780180     Source Type: Journal    
DOI: 10.1016/j.jmbbm.2011.06.002     Document Type: Article

References (49)

1. Bensamoun S., Fan Z., Brice I., Rho J.Y., Ho Ba Tho M.C. Assessment of mechanical properties of human osteon lamellae exhibiting various degrees of mineralization by nanoindentation. J. Muscoskelet. Res. 2008, 11:135-143.
2. Carden A., Rajachar R.M., Morris M.D., Kohn D.H. Ultrastructural changes accompanying the mechanical deformation of bone tissue: a raman imaging study. Calcif. Tissue Int. 2003, 72:166-175.
3. Carnelli D., Gastaldi D., Sassi V., Contro R., Ortiz C., Vena P. A finite element model for direction-dependent mechanical response to nanoindentation of cortical bone allowing for anisotropic post-yield behaviour of the tissue. J. Biomech. Eng. 2010, 132:081008.1-081008.10.
4. Carnelli D., Lucchini R., Ponzoni M., Contro R., Vena P. Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response. J. Biomech. 2011, 10.1016/j.jbiomech.2011.04.020.
5. Carnelli, D., Vena, P., Dao, M., Yao, H., Ortiz, C., Contro, R., 2011b. Orientation and size dependent mechanical modulation within individual osteons in cortical bone tissue. Acta Biomater. (submitted for publication).
6. Cowin S.C. Bone Mechanics 1989, CRC, Boca Raton, FL.
7. Cowin S.C. Bone Mechanics Handbook 2001, CRC Press Inc. 2nd ed.
8. Currey J.D. The Mechanical Adaptations of Bones 1984, Princeton University Press, New Jersey.
9. Currey J.D. Bones: Structure and Mechanics 2002, Princeton University Press, New Jersey.
10. De Borst R., Sluys L.J., Hühlhaus H.B., Pamin J. Fundamental issues in finite element analysis of localization of deformation. Eng. Comput. 1993, 10:99-121.
11. Delafargue A., Ulm F.-J. Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters. Internat. J. Solids Structures 2004, 41:7351-7360.
12. Ebenstein D.M., Pruitt L.A. Nanoindentation of biological materials. Nano Today 2006, 1:26-33.
13. Fan Z., Rho J., Swadener J.G. Three-dimensional finite element analysis of the effects of anisotropy on bone mechanical properties measured by nanoindentation. J. Mater. Res. 2004, 19:114-123.
14. Fantner G., Hassenkam T., Kindt J.H., Weaver J.C., Birkedal H., Pechenik L., Cutroni J.A., Cidade G.A.G., Stucky G.D., Morse D.E., Hansma P.K. Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. Nat. Mater. 2005, 4:612-616.
15. Fratzl P., Gupta H.S., Paschalis E.P., Roschger P. Structure and mechanical quality of the collagen-mineral nano-composite in bone. J. Mater. Chem. 2004, 14:2115-2123.
16. Fratzl P., Weinkamer R. Nature's hierarchical materials. Prog. Mater. Sci. 2007, 52:1263-1334.
17. Fritsch A., Hellmich C. Universal microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity. J. Theoret. Biol. 2007, 244:597-620.
18. Gao H., Huang Y., Nix W.D., Hutchinson J.W. Mechanism-based strain gradient plasticity-I. Theory. J. Mech. Phys. Solids 1999, 47:1239-1263.
19. Garcia D., Zysset P.K., Charlebois M., Curnier A. A three-dimensional elastic-plastic damage constitutive law for bone tissue. Biomech. Model. Mechanobiol. 2009, 8:149-165.
20. Gupta H.S., Stachewicz U., Wagermaier W., Roschger P., Wagner H.D., Fratzl P. Mechanical modulation at the lamellar level in osteonal bone. J. Mater. Res. 2006, 21:1913-1921.
21. Gupta H.S., Wagermaier W., Zickler G.A., Aroush D.R.B., Funari S.S., Roschger P., Wagner H.D., Fratzl P. Nanoscale deformation mechanisms in bone. Nano Lett. 2005, 5:2108-2111.
22. Gupta H.S., Wagermaier W., Zickler G.A., Hartmann J., Funari S.S., Roschger P., Wagner H.D., Fratzl P. Fibrillar level fracture in bone beyond the yield point. Int. J. Fract. 2006, 139:425-436.
23. Hengsberger S., Kulik A., Zysset P. Nanoindentation discriminates the elastic properties of individual human bone lamellae under dry and physiological conditions. Bone 2002, 30:178-184.
24. Jager I., Fratzl P. Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles. Biophys. J. 2000, 79:1737-1746.
25. Jepsen K.J., Davy D.T. Comparison of damage accumulation measures in human cortical bone. J. Biomech. 1997, 30:891-894.
26. Keaveny T.M., Wachtel E.F., Guo X.E., Hayes W.C. Mechanical behavior of damaged trabecular bone. J. Biomech. 1994, 27:1309-1318.
27. Kotha S.P., Guzelsu N. Tensile damage and its effects on cortical bone. J. Biomech. 2003, 36:1683-1689.
28. Krajcinovic D. Damage Mechanics. North-Holland Series in Applied Mathematics and Mechanics 1996, Elsevier, Amsterdam, The Netherlands.
29. Lewis G., Nyman J.S. The use of nanoindentation technique for characterizing the properties of mineralized hard tissues: state-of-the art review. J. Biomed. Mater. Res. Part B 2008, 87B:286-301.
30. Mercer C., He M.Y., Wang R., Evans A.G. Mechanisms governing the inelastic deformation of cortical bone and application to trabecular bone. Acta Biomater. 2006, 2:59-68.
31. Mullins L.P., Bruzzi M.S., McHugh P.E. Calibration of a constitutive model for the post-yield behaviour of cortical bone. J. Mech. Behav. Biomed. Mater. 2009, 2:460-470.
32. Niebur G.L., Feldstein M.J., Yuen J.C., Chen T.J., Keaveny T.M. High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone. J. Biomech. 2000, 33:1575-1583.
33. Nix W.D., Gao H. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 1998, 46:411-425.
34. Olesiak S.E., Oyen M.L., Ferguson V.L. Viscous-elastic-plastic behavior of bone using Berkovich nanoindentation. Mech. Time-Depend. Mater. 2010, 14:111-124.
35. Oliver W.C., Pharr G.M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 1992, 7:1564-1583.
36. Paietta R.C., Campbell S.E., Ferguson V.L. Influences of spherical tip radius, contact depth, and contact area on nanoindentation properties of bone. J. Biomech. 2011, 44:285-290.
37. Ramtani S., Zidi M. A theoretical model of the effect of continuum damage on a bone adaptation model. J. Biomech. 2001, 34:471-479.
38. Rho J.Y., Kuhn-Spearing L., Zioupos P. Mechanical properties and the hierarchical structure of bone. Med. Eng. Phys. 1998, 20:92-102.
39. Rho J., Tsui T.Y., Pharr G.M. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials 1997, 18:1325-1330.
40. Rho J., Zioupos P., Currey J.D., Pharr G.M. Microstructural elasticity and regional heterogeneity in human femoral bone of various ages examined by nano-indentation. J. Biomech. 2002, 35:189-198.
41. Tai K., Qi H.J., Ortiz C. Effect of mineral content on the nanoindentation properties and nanoscale deformation mechanisms of bovine tibial cortical bone. J. Mater. Sci. Mater. Med. 2005, 16:947-959.
42. Tai K., Ulm F.-J., Ortiz C. Nanogranular origins of the strength of bone. Nano Lett. 2006, 6:2520-2525.
43. Wagermaier W., Gupta H.S., Gourrier A., Paris O., Roschger P., Burghammer M., Riekel C., Fratzl P. Scanning texture analysis of lamellar bone using microbeam synchrotron x-ray radiation. J. Appl. Crystallogr. 2007, 40:115-120.
44. Weiner S., Addadi L., Wagner H.D. Materials design in biology. Mater. Sci. Eng. C 2000, 11:1-8.
45. Weiner S., Wagner H.D. The material bone: structure mechanical function relations. Annu. Rev. Mater. Sci. 1998, 28:271-298.
46. Yao H., Dao M., Carnelli D., Tai K., Ortiz C. Size-dependent heterogeneity benefits the mechanical performance of bone. J. Mech. Phys. Solids 2011, 59:64-74.
47. Zhang J., Michalenko M.M., Kuhl E., Ovaert T.C. Characterization of indentation response and stiffness reduction of bone using a continuum damage model. J. Mech. Behav. Biomed. Mater. 2010, 3:189-202.
48. Zhang J., Niebur G.L., ovaert T.C. Mechanical property determination of bone through nano- and micro-indentation testing and finite element simulation. J. Biomech. 2008, 41:267-275.
49. Zysset P.K., Guo E.X., Hoffler E.C., Moore K.E., Goldstein S.A. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J. Biomech. 1999, 32:1005-1012.