Abstract
The aim of this study is to investigate the change of mechanical properties of human dentin due to aging and spatial variation. Sections of coronal dentin are made from human molars in three groups: young, mid-aged, and old patients. A nanoindentation test is conducted from regions near the pulp to the dentin-enamel junction (DEJ) to evaluate the load-depth indentation response and determine Young’s modulus and hardness. Based on the loading and unloading load-displacement curves in nanoindentation, a numerical model of plastic damage is used to study the plastic and the damage behaviors and the contribution to the degradation in the unloading stiffness. The experimental results show that Young’s modulus of the inner dentin is significantly lower than that of outer dentin in each age group. Compared with the young dentin, the old dentin has greater hardness and Young’s modulus with similar spatial variations. The magnitudes of the yield strength and the damage variable are also affected by aging and vary with spatial locations. In the same age group, the yield strength in inner dentin is lower than those in middle and outer dentin, more damage occurs with similar spatial variations, and the yield strength of young dentin is generally lower and more damage compared with those in both the mid-aged and old groups.
Similar content being viewed by others
References
Pashley, D. Dynamics of the pulpo-dentin complex. Critical Reviews in Oral Biology and Medicine, 7(2), 104–133 (1996)
Marshall, G. W., Marshall, S. J., Kinney, J. H., and Balooch, M. The dentin substrate: structure and properties related to bonding. Journal of Dentistry, 25(6), 441–458 (1997)
Pashley, D., Okabe, A., and Parham, P. The relationship between dentin microhardness and tubule density. Dental Traumatology, 1(5), 176–179 (1985)
Marshall, G. W., Habelitz, S., Gallagher, R., Balooch, M., Balooch, G., and Marshall, S. J. Nanomechanical properties of hydrated carious human dentin. Journal of Dental Research, 80(8), 1768–1771 (2001)
Oyen, M. L. Nanoindentation hardness of mineralized tissues. Journal of Biomechanics, 39(14), 2699–2702 (2006)
Ziskind, D., Hasday, M., Cohen, S. R., and Wagner, H. D. Young’s modulus of peritubular and intertubular human dentin by nano-indentation tests. Journal of Structural Biology, 174(1), 23–30 (2011)
Senawongse, P., Otsuki, M., Tagami, J., and Mjör, I. Age-related changes in hardness and modulus of elasticity of dentine. Archives of Oral Biology, 51(6), 457–463 (2006)
Tesch, W., Eidelman, N., Roschger, P., Goldenberg, F., Klaushofer, K., and Fratzl, P. Graded microstructure and mechanical properties of human crown dentin. Calcified Tissue International, 69, 147–157 (2001)
Zhang, J., Niebur, G. L., and Ovaert, T. C. Mechanical property determination of bone through nano- and micro-indentation testing and finite element simulation. Journal of Biomechanics, 41(2), 267–275 (2008)
Yao, H. M., Dao, M., Imholt, T., Huang, J., Wheeler, K., Bonilla, A., Suresh, S., and Ortiz, C. Protection mechanisms of the iron-plated armor of a deep-sea hydrothermal vent gastropod. Proceedings of the National Academy of Sciences of the United States of America, 107(3), 987–992 (2010)
Carnelli, D., Lucchini, R., Ponzoni, M., Contro, R., and Vena, P. Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response. Journal of Biomechanics, 44(10), 1852–1858 (2011)
An, B., Wang, R., Arola, D., and Zhang, D. The role of property gradients on the mechanical behavior of human enamel. Journal of the Mechanical Behavior of Biomedical Materials, 9, 63–72 (2012)
Schwiedrzik, J. J. and Zysset, P. K. An anisotropic elastic-viscoplastic damage model for bone tissue. Biomechanics and Modeling in Mechanobiology, 12(2), 201–213 (2013)
Fan, Z. and Rho, J. Y. Three-dimensional finite element analysis of the effects of anisotropy of bone mechanical properties measured by nanoindentation. Journal of Materials Research, 19(1), 114–123 (2004)
Tai, K., Ulm, F. J., and Ortiz, C. Nanogranular origins of the strength of bone. Nano Letters, 6(11), 2520–2525 (2006)
Carnelli, D., Gastaldi, D., Sassi, V., Contro, R., Ortiz, C., and Vena P. 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, 132(8), 081008 (2010)
Mullins, L., Bruzzi, M., and McHugh, P. Calibration of a constitutive model for the post-yield behaviour of cortical bone. Journal of the Mechanical Behavior of Biomedical Materials, 2, 460–470 (2009)
Schwiedrzik, J. J. and Zysset, P. K. The influence of yield surface shape and damage in the depthdependent response of bone tissue to nanoindentation using spherical and Berkovich indenters. Computer Methods in Biomechanics and Biomedical Engineering, 18(5), 492–505 (2015)
Zioupos, P., Hansen, U., and Currey, J. D. Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure. Journal of Biomechanics, 41(14), 2932–2939 (2008)
Zhao, Y., Wu, Z., Turner, S., MacLeay, J., Niebur, G. L., and Ovaert, T. C. Indentation experiments and simulation of ovine bone using a viscoelastic-plastic damage model. Journal of Materials Research, 27(1), 368–377 (2012)
Olesiak, S. E., Oyen, M. L., and Ferguson, V. L. Viscous-elastic-plastic behavior of bone using Berkovich nanoindentation. Mechanics of Time-Dependent Materials, 14(2), 111–124 (2010)
Oyen, M. L. and Ko, C. C. Examination of local variations in viscous, elastic, and plastic indentation responses in healing bone. Journal of Materials Science: Materials in Medicine, 8(4), 623–628 (2007)
Lucchini, R., Carnelli, D., Ponzoni, M., Bertarelli, E., Gastaldi, D., and Vena, P. Role of damage mechanics in nanoindentation of lamellar bone at multiple sizes: experiments and numerical modeling. Journal of the Mechanical Behavior of Biomedical Materials, 4, 1852–1863 (2011)
An, B., Wang, R., and Zhang, D. Region-dependent micro damage of enamel under indentation. Acta Mechanica Sinica, 28(6), 1651–1658 (2012)
Habelitz, S., Marshall, G. W., Balooch, M., and Marshall, S. J. Nanoindentation and storage of teeth. Journal of Biomechanics, 35(7), 995–998 (2002)
Doerner, M. F. and Nix, W. D. A method for interpreting the data from depth-sensing indentation instruments. Journal of Materials Research, 1(4), 601–609 (1986)
Oliver, W. C. and Pharr, G. M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiment. Journal of Materials Research, 7(6), 1564–1583 (1992)
Dao, M., Chollacoop, N., van Vliet, K. J., Venkatesh, T. A., and Suresh, S. Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Materialia, 49(19), 3899–3918 (2001)
Bruet, B., Song, J., Boyce, M. C., and Ortiz, C. Materials design principles of ancient fish armor. Nature Materials, 7, 748–756 (2008)
Lubliner, J., Oliver, J., Oller, S., and Oñate, E. A plastic-damage model for concrete. International Journal of Solids and Structures, 25(3), 299–326 (1989)
Lee, J. and Fenves, G. L. Plastic-damage model for cyclic loading of concrete structures. Journal of Engineering Mechanics, 124(8), 892–900 (1998)
Zhang, J., Michalenko, M. M., Kuhl, E., and Ovaert, T. C. Characterization of indentation response and stiffness reduction of bone using a continuum damage model. Journal of the Mechanical Behavior of Biomedical Materials, 3, 189–202 (2010)
Kinney, J. H., Balooch, M., Marshall, S. J., Marshall, G. W., and Weihs, T. P. Hardness and Young’s modulus of human peritubular and intertubular dentin. Archives of Oral Biology, 41(1), 9–13 (1996)
Angker, L., Swain, M. V., and Kilpatrick, N. Micro-mechanical characterization of the properties of primary tooth dentine. Journal of Dentistry, 31(4), 261–267 (2003)
Angker, L., Swain, M. V., and Kilpatrick, N. Characterising the micro-mechanical behaviour of the carious dentine of primary teeth using nano-indentation. Journal of Biomechanics, 38(7), 1535–1542 (2005)
Pugach, M. K., Strother, J., Darling, C. L., Fried, D., Gansky, S. A., Marshall, S. J., and Marshall, G. W. Dentin caries zones: mineral, structure, and properties. Journal of Dentin Research, 88(1), 71–76 (2009)
Nalla, R. K., Porter, A. E., Daraio, C., Minor, A. M., Radmilovic, V., Stach, E. A., Tomsia, A. P., and Ritchie, R. O. Ultrastructural examination of dentin using focused ion-beam cross-sectioning and transmission electron microscopy. Micron, 36, 672–680 (2005)
Arola, D. Fracture and aging in dentin. Dental Biomaterials: Imaging, Testing and Modeling (eds. Curtis, R. V. and Wation, T. F.), Woodhead Publishing, Cambridge, 314–340 (2007)
Porter, A. E., Nalla, R. K., Minor, A., Jinschek, J. R., Kisielowski, C., Radmilovic, V., Kinney, J. H., Tomsia, A. P., and Ritchie, R. O. A transmission electron microscopy study of mineralization in age-induced transparent dentin. Biomaterials, 26(36), 7650–7660 (2005)
Kinney, J. H., Nalla, R. K., Pople, J. A., Breunig, T. M., and Ritchie, R. O. Age-related transparent root dentin: mineral concentration, crystallite size, and mechanical properties. Biomaterials, 26(16), 3363–3376 (2005)
Eltit, F., Ebacher, V., and Wang, R. Inelastic deformation and microcracking process in human dentin. Journal of Structural Biology, 183(2), 141–148 (2013)
Nazari, A., Bajaj, D., Zhang, D., Romberg, E., and Arola, D. Aging and the reduction in fracture toughness of human dentin. Journal of the Mechanical Behavior of Biomedical Materials, 2, 550–559 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 11172161 and 11372173), the Innovation Program of Shanghai Municipal Education Commission (No. 12ZZ092), the China Postdoctoral Science Foundation (No. 2013M541504), and the Shanghai Leading Academic Discipline Project (No. S30106)
Rights and permissions
About this article
Cite this article
Li, X., An, B. & Zhang, D. Determination of elastic and plastic mechanical properties of dentin based on experimental and numerical studies. Appl. Math. Mech.-Engl. Ed. 36, 1347–1358 (2015). https://doi.org/10.1007/s10483-015-1987-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-015-1987-9