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Effect of dentin tubules on the mechanical properties of dentin. Part I: Stress-strain relations and strength criterion

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Abstract

As known, there is a large number of dentin tubules in dentin. These tubules have varying radii and are shaped into radially parallel pattern. The anisotropy of microstructure of dentin shows that dentin should be treated as a material of varying transverse isotropy. In this Part, the elastic stress-strain relations and the quadratic strength criterion are established in the form of having varying transverse isotropy, in the framework of micromechanics to take into account of the effect of the microstructures-dentin tubules. Simplified forms for isotropic and homogeneous cases, as well as the corresponding plane stress form of the stress-strain relations are also given. These theoretical models are very well supported by the experiments shown later in the continued paper (Part II).

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References

  1. Mjör IA, Fejerskov O. Human Oral Embryology and Histology. Copenhagen: Munksgaard, 1986.

    Google Scholar 

  2. Peyton FA, Mahier DB, Hershenov. Physical properties of dentine.J. dent Res, 1952, 31(3): 366–370

    Google Scholar 

  3. Craig RG, Peyton FA. Elastic and mechanical properties of human dentin.J dent Res, 1958, 37(4):710–718

    Google Scholar 

  4. Renson CE, Boyde A, Jones SJ. Scanning electron microscopy of human dentine specimens fractured in bend and torsion tests.Archs Oral Biol, 1974, 19: 447–450

    Article  Google Scholar 

  5. Renson CE, Braden M. Experimental determination of the rigidity modulus, Poisson's ratio and elastic limit in shear of human dentine.Archs Oral Biol, 1975, 20: 43–47

    Article  Google Scholar 

  6. Rasmussen ST, Patchin RE, Scott DB, Hever AH. Fracture properties of human enamel and dentin.J Dent Res, 1976, 55: 154–164

    Google Scholar 

  7. Wang RZ, Weiner S. Strain-structure relations in human teeth using moire fringes.Journal of Biomechanics, 1998, 31: 135–141

    Article  Google Scholar 

  8. Meredith N, Sherriff M, Setchell DJ, Swanson SAV. Measurement of the microhardness and Young's modulus of human enamel and dentine using an indentation technique.Archs Oral Biol, 1996, 41(6): 539–545

    Article  Google Scholar 

  9. Kinney JH, Balooch M, Marshall SJ, Marshall WJR, Weih TP. Hardness and Young's modulus of human peritubular and intertubular dentine.Archs Oral Biol, 1996, 41(1): 9–13

    Article  Google Scholar 

  10. Wentrup-Byrne E, Armstrong CA, Armstrong RS, Collins M. Fourier transform raman microscopic mapping of the molecular components in a human tooth.Journal of Raman Spectroscopy, 1997, 28: 151–158

    Article  Google Scholar 

  11. Zheng QS, Du DX. Close-form interacting solutions for overall elastic moduli of composite materials with multi-phase inclusions, holes and microcracks.Key Engineering Materials, 1998, 145–149, Part 1: 479–488

    Article  Google Scholar 

  12. Nemat-Nasser S, Hori M. Micromechanics: overall properties of heterogeneous materials. New York: North-Holland, 1993

    MATH  Google Scholar 

  13. Mura T. Micromechanics of defects in solids. The Netherlands: Martinus Nijhoff Publishers, 1987: 80

    Google Scholar 

  14. Backus, G. A geometrical picture of anisotropic elastic tensors.Review Geophys Spacephys. 1970, 8: 633–671

    Google Scholar 

  15. Spencer, AJM. A note on the decomposition of tensors into traceless symmetric tensors.Int J Engng Sci, 1970, 8: 475–481

    Article  MATH  Google Scholar 

  16. Cowin, SC. Properties of the anisotropic elasticity tensor.Q J Mech Appl Math, 1989, 42: 249–266

    MATH  MathSciNet  Google Scholar 

  17. Zheng QS. Theory of representations for tensor functions—A unified invariant approach to constitutive equations.Appl Mech Rev, 1994, 47(11): 545–587

    Article  MATH  Google Scholar 

  18. Rogers TG. Yield criteria, flow rules, and hardening in anisotropic plasticity.Yielding, Damage, and Failure of Anisotropic Solids, EGF5 (Edited by Boehler JP), London, Mechanical Engineering Publications, 1990: 53–79

    Google Scholar 

  19. Cui L, Cheng AHD, Abousleiman Y. Poroelastic solution for an inclined borehole.Journal of Applied Mechanics, 1997, 65: 32–38

    Google Scholar 

  20. Wen M, Zheng QS, Du DX. Some basic problems in numerically simulating effective properties and local fields of composite materials.Acta Mechanica Solida Sinica, 1999, 3 (to be published)

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Correspondence to Zheng Quanshui.

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The project supported by the National Natural Science Foundation of China (19525207).

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Bo, H., Quanshui, Z. Effect of dentin tubules on the mechanical properties of dentin. Part I: Stress-strain relations and strength criterion. Acta Mech Sinica 15, 355–365 (1999). https://doi.org/10.1007/BF02487933

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  • DOI: https://doi.org/10.1007/BF02487933

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