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An Experimentally Validated Micromechanical Model for Elasticity and Strength of Hydroxyapatite Biomaterials

Published online by Cambridge University Press:  15 March 2011

Andreas Fritsch ,
Luc Dormieux ,
Christian Hellmich  and
Julien Sanahuja
Andreas Fritsch
Affiliation:
Vienna University of Technology (TU Wien), Karlsplatz 13, A-1040 Wien, Austria Ecole Nationale des Ponts et Chaussess, 6-8 av. Blaise Pascal, 77455 Marne-la-Vallee, France
Luc Dormieux
Affiliation:
Ecole Nationale des Ponts et Chaussess, 6-8 av. Blaise Pascal, 77455 Marne-la-Vallee, France
Christian Hellmich
Affiliation:
Vienna University of Technology (TU Wien), Karlsplatz 13, A-1040 Wien, Austria
Julien Sanahuja
Affiliation:
Électricité de France, Route de Sens, Ecuelles, 77818 Moret sur Loing, France
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Abstract

Hydroxyapatite biomaterials production has been a major field in biomaterials science and biomechanical engineering. As concerns prediction of their stiffness and strength, we propose to go beyond statistical correlations with porosity or empirical structure-property relationships, as to resolve the material-immanent microstructures governing the overall mechanical behavior. The macroscopic mechanical properties are estimated from the microstructures of the materials and their composition, in a homogenization process based on continuum micromechanics. Thereby, biomaterials are envisioned as porous polycrystals consisting of hydroxyapatite needles and spherical pores. Validation of respective micromechanical models relies on two independent experimental sets: Biomaterial-specific macroscopic (homogenized) stiffness and uniaxial (tensile and compressive) strength predicted from biomaterial-specific porosities, on the basis of biomaterial-independent (‘universal') elastic and strength properties of hydroxyapatite, are compared to corresponding biomaterial-specific experimentally determined (acoustic and mechanical) stiffness and strength values. The good agreement between model predictions and the corresponding experiments underlines the potential of micromechanical modeling in improving biomaterial design, through optimization of key parameters such as porosities or geometries of microstructures, in order to reach desired values for biomaterial stiffness or strength.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1132: Symposium Z – Mechanics of Biological and Biomedical Materials , 2008 , 1132-Z06-03
Copyright
Copyright © Materials Research Society 2009

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References

REFERENCES

1. Hench, L.L. and Jones, R.J. (Eds.), Biomaterials, artifical organs and tissue engineering, (Woodhead Publishing, Cambridge, 2005).Google Scholar
2. Dorozhkin, S.V. and Epple, M., Angew. Chem. Int. Ed. 41, 3130 (2002).Google Scholar
3. Charrière, E., Terrazzoni, S., Pittet, C., Mordasini, P., Dutoit, M., Lemaître, J. and Zysset, P., Biomaterials 22, 2937 (2001).Google Scholar
4. Frame, J.W., Browne, R.M. and Brady, C.L., Biomaterials 2, 19 (1981).Google Scholar
5. Mastrogiacomo, M., Scaglione, S., Martinetti, R., Dolcini, L., Beltrame, F., Cancedda, R. and Quarto, R. R, Biomaterials 27, 3230 (2006).Google Scholar
6. Verma, D., Katti, K. and Katti, D., J. Biomed. Mater. Res. 78A, 772 (2006).Google Scholar
7. Peelen, J., Rejda, B. and Groot, K. de, Ceramurgia Int. 4, 71 (1978).Google Scholar
8. Akao, M., Aoki, H. and Kato, K., J. Mater. Sci. 16, 809 (1981).Google Scholar
9. With, G. De, Dijk, H. van, Hattu, N. and Prijs, K., J. Mater. Sci. 16, 1592 (1981).Google Scholar
10. Shareef, M., Messer, P. and Noort, R., Biomaterials 14, 69 (1993).Google Scholar
11. Arita, I., Wilkinson, D., Mondragón, M. and Castaño, V., Biomaterials 16, 403 (1995).Google Scholar
12. Martin, R.I. and Brown, P.W., J. Mater. Sci.: Mater. Med. 6, 138 (1995).Google Scholar
13. Fritsch, A., Dormieux, L., Hellmich, C. and Sanahuja, J., J. Biomed. Mater. Res. 88A, 149 (2009).Google Scholar
14. Liu, D.-M., Ceramics Int. 24, 441 (1998).Google Scholar
15. Rao, W. and Boehm, R., J. Dent. Res. 53, 1351 (1974).Google Scholar
16. Driessen, A., Klein, C. and Groot, K. de, Biomaterials 3, 113 (1982).Google Scholar
17. Katz, J.L. and Harper, R., in Concise encyclopedia of medical and dental materials, edited by Williams, D. (Pergamon Press, Oxford, 1990), p. 87.Google Scholar
18. Hill, R., J. Mech. Phys. Solids 11, 357 (1963).Google Scholar
19. Hashin, Z., J. Appl. Mech. 29, 143 (1983).Google Scholar
20. Suquet, P. (Ed.), Continuum micromechanics (Springer, Wien - New York, 1997).Google Scholar
21. Zaoui, A., J. Eng. Mech. 128, 808 (2002).Google Scholar
22. Eshelby, J.D., Proc. R. Soc. Lond., Ser. A 241, 376 (1957).Google Scholar
23. Benveniste, Y., Mech. Mater. 6, 147 (1987).Google Scholar
24. Mori, T. and Tanaka, K., Acta Metallurgica 21, 571 (1973).Google Scholar
25. Hershey, A.V., J. Appl. Mech. 21, 236 (1954).Google Scholar
26. Kröner, E., Z. Phys. 151, 504 (1958).Google Scholar
27. Fritsch, A., Dormieux, L. and Hellmich, C., Comptes Rendus Mecanique 334, 151 (2006).Google Scholar
28. Salençon, J., Handbook of continuum mechanics: general concepts, thermoelasticity (Springer, Berlin, 2001).Google Scholar
29. Hellmich, C. and Ulm, F.J., J. Eng. Mech. 128, 898 (2002).Google Scholar
30. Hellmich, C., Barthélémy, J.-F. and Dormieux, L., Eur. J. Mech. A: Solids 23, 783 (2004).Google Scholar
31. Fritsch, A. and Hellmich, C., J. Theor. Biol. 244, 597 (2007).Google Scholar
32. Hofstetter, K., Hellmich, C. and Eberhardsteiner, J., Eur. J. Mech. A: Solids 24, 1030 (2005).Google Scholar
33. Katz, J.L. and Ukraincik, K., J. Biomech. 4, 221 (1971).Google Scholar
34. Gilmore, R. and Katz, J.L., J. Mater. Sci. 17, 1131 (1982).Google Scholar
35. Ashman, R.B., Cowin, S.C., Buskirk, W.C. Van and Rice, J.C., J. Biomech. 17, 349 (1984).Google Scholar
36. Ashman, R.B., Corin, J.D. and Turner, C.H., J. Biomech. 20, 979 (1987).Google Scholar
37. Carcione, J.M., Wave fields in real media: wave propagation in anisotropic, anelastic and porous media (Pergamon, Oxford, 2001).Google Scholar
38. Kolsky, H., Stress waves in solids (Clarendon Press, Oxford, 1953).Google Scholar
39. Pichler, B., Hellmich, C. and Mang, H.A., Int. J. Numerical Anal. Methods Geomech. 31, 111 (2007).Google Scholar
40. Pichler, B., Hellmich, C. and Dormieux, L., in Bifurcations, Instabilities, Degradation in Geomechanics, edited by Exadaktylos, G.E. and Vardoulakis, I.G. (Springer, Berlin, 2007), p. 245.Google Scholar
41. Woodard, J.R., Hilldore, A.J., Lan, S.K., Park, C.J., Morgan, A.W., Eurell, J.A.C., Clark, S.G., Wheeler, M.B., Jamison, R.D. and A.J. Wagoner Johnson, Biomaterials 28, 45 (2007).Google Scholar
42. Yunoki, S., Ikoma, T., Monkawa, A., Ohta, K., Kikuchi, M., Sotome, S., Shinomiya, K. and Tanaka, J., Mater. Lett. 60, 999 (2006).Google Scholar
43. Salgado, A.J., Coutinho, O.P. and Reis, R.L., Macromol. Biosci. 4, 743 (2004).Google Scholar