Russian Journal of Biological Physics and Chemisrty Russian Journal of Biological Physics and Chemisrty АКТУАЛЬНЫЕ ВОПРОСЫ БИОЛОГИЧЕСКОЙ ФИЗИКИ И ХИМИИ 2499-9962 54328 Моделирование в биофизике Modelling in biophycis Моделирование в биофизике POISSON'S RATIO OF DENTIN AND ENAMEL AS ANISOTROPIC MEDIA WITH HEXAGONAL SYMMETRY POISSON'S RATIO OF DENTIN AND ENAMEL AS ANISOTROPIC MEDIA WITH HEXAGONAL SYMMETRY Muslov S A Muslov S A muslov@mail.ru Evdokimov Moscow State Medical Stomatological University (MSMSU) ru Evdokimov Moscow State Medical Stomatological University (MSMSU) ru 25 09 2018 25 09 2018 3 3 561 567 20 09 2018 20 09 2018 https://rusjbpc.ru/en/nauka/article/54328/view

In this paper, the orientation dependence of the Poisson's ratio of teeth’s dentin and enamel on the basis of matrices of elastic constants and the compliance coefficients of hexagonal crystals, such as crystals of dentine hydroxyapatite, was obtained for the first time. The results of calculating the Poisson's ratios of dentin and enamel as a crystalline system with a hexagonal structure are presented in the form of tables and diagrams in the polar and Cartesian coordinate systems. It is shown that the maximum value of the Poisson's ratio of dentin (0.54) is greater than the upper limit for the Poisson's ratio of isotropic materials, including known restoration materials, which in some cases may reduce the quality of restorations. The effective elastic characteristics of dentine and enamel, including Poisson's ratio using different averaging methods, are calculated.

In this paper, the orientation dependence of the Poisson's ratio of teeth’s dentin and enamel on the basis of matrices of elastic constants and the compliance coefficients of hexagonal crystals, such as crystals of dentine hydroxyapatite, was obtained for the first time. The results of calculating the Poisson's ratios of dentin and enamel as a crystalline system with a hexagonal structure are presented in the form of tables and diagrams in the polar and Cartesian coordinate systems. It is shown that the maximum value of the Poisson's ratio of dentin (0.54) is greater than the upper limit for the Poisson's ratio of isotropic materials, including known restoration materials, which in some cases may reduce the quality of restorations. The effective elastic characteristics of dentine and enamel, including Poisson's ratio using different averaging methods, are calculated.

 enamel dentin Poisson's ratio crystals of hydroxyapatite enamel dentin Poisson's ratio crystals of hydroxyapatite

Belomestnykh V.N., Tesleva E.P. Poisson's ratio and the Grüneisen parameter of solids. Bulletin of the Tomsk Polytechnic University, 2003, vol. 306, no. 5, pp. 8-12. Belomestnykh V.N., Tesleva E.P. Poisson's ratio and the Grüneisen parameter of solids. Bulletin of the Tomsk Polytechnic University, 2003, vol. 306, no. 5, pp. 8-12. Goldstein R.V., Gorodtsov A., Lisovenko D.S. Variability of elastic properties of hexagonal auxetics. DAN, 2011, vol. 441, no. 4, pp. 468-471. Goldstein R.V., Gorodtsov A., Lisovenko D.S. Variability of elastic properties of hexagonal auxetics. DAN, 2011, vol. 441, no. 4, pp. 468-471. Ivanov G.P., Lebedev T.A. On the physical sense of the Poisson's ratio. Proceedings of Leningr. polytechnic. in-ta named M.I. Kalinina, 1964, vol. 236, pp. 38-46. Ivanov G.P., Lebedev T.A. On the physical sense of the Poisson's ratio. Proceedings of Leningr. polytechnic. in-ta named M.I. Kalinina, 1964, vol. 236, pp. 38-46. Lebedenko I.Yu., Arutyunov S.D., Muslov S.A., Useinov A.S. Nanohardness and Young's modulus of tooth enamel. Vestnik RUDN, series Medicine, 2009, vol. 4, pp. 637-638. Lebedenko I.Yu., Arutyunov S.D., Muslov S.A., Useinov A.S. Nanohardness and Young's modulus of tooth enamel. Vestnik RUDN, series Medicine, 2009, vol. 4, pp. 637-638. Lebedenko I.Yu., Arutyunov S.D., Muslov S.A., Useinov A.S. Winter Study of nanomechanical properties of tooth enamel. Chair, 2010, vol. 32, pp. 24-28. Lebedenko I.Yu., Arutyunov S.D., Muslov S.A., Useinov A.S. Winter Study of nanomechanical properties of tooth enamel. Chair, 2010, vol. 32, pp. 24-28. Lebedenko I.Yu., Arutyunov S.D., Muslov S.A., Bolataev Z.B. Elastic anisotropy of the hard tissues of the tooth. Proceedings of the Eurasian Congress of medical physics and engineering “MEDICAL PHYSICS-2010”, June 21-25, 2010. Moscow State University, 2010, vol. l, pp. 279-280. Lebedenko I.Yu., Arutyunov S.D., Muslov S.A., Bolataev Z.B. Elastic anisotropy of the hard tissues of the tooth. Proceedings of the Eurasian Congress of medical physics and engineering “MEDICAL PHYSICS-2010”, June 21-25, 2010. Moscow State University, 2010, vol. l, pp. 279-280. Lebedenko I.Yu., Arutyunov S.D., Useinov A.S., Muslov S.A., Brandt N.N., Apresyan S.V. Study of the effect of ultralow (4.2 K) temperatures on the nanomechanical properties of tooth enamel. Proceedings of the Eurasian Congress of medical physics and engineering “MEDICAL PHYSICS-2010”, June 21-25, 2010, Moscow State University, vol. 4, part I, pp. 323-324. Lebedenko I.Yu., Arutyunov S.D., Useinov A.S., Muslov S.A., Brandt N.N., Apresyan S.V. Study of the effect of ultralow (4.2 K) temperatures on the nanomechanical properties of tooth enamel. Proceedings of the Eurasian Congress of medical physics and engineering “MEDICAL PHYSICS-2010”, June 21-25, 2010, Moscow State University, vol. 4, part I, pp. 323-324. Nye D. Physical properties of crystals. M: IL, 1960, 385 p. Nye D. Physical properties of crystals. M: IL, 1960, 385 p. Pertsov S.S., Stureva G.M., Muslov S.A., Sinitsyn A.A., Korneev A.A., Zaitseva N.V. The basics of biomechanics for the dentists. M: MSMSU, 2017, 115 p. Pertsov S.S., Stureva G.M., Muslov S.A., Sinitsyn A.A., Korneev A.A., Zaitseva N.V. The basics of biomechanics for the dentists. M: MSMSU, 2017, 115 p. Khyshiktuyev B.S., Khyshiktueva N. Biochemistry of the oral cavity. Chita, 2004, 84 p. Khyshiktuyev B.S., Khyshiktueva N. Biochemistry of the oral cavity. Chita, 2004, 84 p. Goldstein R.V., Gorodtsov V.A., Komarov A.M., Lisovenko D.S. Extreme values of the shear modulus for hexagonal crystals. Scripta Mater., 2017, vol. 140, pp. 55-58, DOI: 10.1016/j.scriptamat.2017.07.002. Goldstein R.V., Gorodtsov V.A., Komarov A.M., Lisovenko D.S. Extreme values of the shear modulus for hexagonal crystals. Scripta Mater., 2017, vol. 140, pp. 55-58, DOI: 10.1016/j.scriptamat.2017.07.002. Katz J.L., Ukraincik K. J. Biomech., 1971, vol. 4, p. 221, DOI: 10.1016/0021-9290(71)90007-8. Katz J.L., Ukraincik K. J. Biomech., 1971, vol. 4, p. 221, DOI: 10.1016/0021-9290(71)90007-8. Katz J.L. J. Biomech., 1971, vol. 4, p. 455, DOI: 10.1016/0021-9290 (71)90064-9. Katz J.L. J. Biomech., 1971, vol. 4, p. 455, DOI: 10.1016/0021-9290 (71)90064-9. Lees S., Davidson C.L. The role of collagen in the elastic properties of calcified tissues J. Biomechanics, 1977, vol. 10, no. 8, pp. 473-86. Lees S., Davidson C.L. The role of collagen in the elastic properties of calcified tissues J. Biomechanics, 1977, vol. 10, no. 8, pp. 473-86. Lees S. [et al.] Anisotropy in hard dental tissues J. Biomech. 1972, vol. 5, no. 6, pp. 557-64. Lees S. [et al.] Anisotropy in hard dental tissues J. Biomech. 1972, vol. 5, no. 6, pp. 557-64. Povolo F. [et al.] Poisson's ratio in zirconium single crystals. J. Nuclear Materials 1983, vol. 118, no. 1, pp. 78-82. Povolo F. [et al.] Poisson's ratio in zirconium single crystals. J. Nuclear Materials 1983, vol. 118, no. 1, pp. 78-82. Sew Meng Chung [et al.] Measurement of Poisson’s ratio of dental composite restorative materials. Biomaterials, 2004, vol. 25, pp. 2455-2460. Sew Meng Chung [et al.] Measurement of Poisson’s ratio of dental composite restorative materials. Biomaterials, 2004, vol. 25, pp. 2455-2460. Shermergor T.D. Theory of elasticity of microinhomogeneous mediums. Moscow, Science, 1977, 399 p. Shermergor T.D. Theory of elasticity of microinhomogeneous mediums. Moscow, Science, 1977, 399 p.