Siyong LIU, Yuanzhi XU, Richeng LIAO, Ge HE, Li DING, Bingbing AN, Dongsheng ZHANG . On fracture behavior of inner enamel: a numerical study[J]. Applied Mathematics and Mechanics, 2023 , 44(6) : 931 -940 . DOI: 10.1007/s10483-023-3007-6

[1] YAHYAZADEHFAR, M., ZHANG, D., and AROLA, D. On the importance of aging to the crack growth resistance of human enamel. Acta Biomaterialia, 32, 264–274(2016)
[2] YILMAZ, E. D. and SCHNEIDER, G. A. Mechanical behavior of enamel rods under microcompression. Journal of the Mechanical Behavior of Biomedical Materials, 63, 183–194(2016)
[3] RIVERA, C., AROLA, D., and OSSA, A. Indentation damage and crack repair in human enamel. Journal of the Mechanical Behavior of Biomedical Materials, 21, 178–184(2013)
[4] ESPINOSA, H. D., RIM, J. E., BARTHELAT, F., and BUEHLER, M. J. Merger of structure and material in nacre and bone-perspectives on de novo biomimetic materials. Progress in Materials Science, 54(8), 1059–1100(2009)
[5] LI, X., AN, B., and ZHANG, D. Determination of elastic and plastic mechanical properties of dentin based on experimental and numerical studies. Applied Mathematics and Mechanics (English Edition), 36(10), 1347–1358(2015) https://doi.org/10.1007/s10483-015-1987-9
[6] WANG, R., MAO, S., ROMBERG, E., AROLA, D., and ZHANG, D. Importance of aging to dehydration shrinkage of human dentin. Applied Mathematics and Mechanics (English Edition), 33(3), 333–344(2012) https://doi.org/10.1007/s10483-012-1553-8
[7] XU, Y., AN, B., ZHANG, D., and WANG, R. Region dependent fracture resistance behavior of human dentin based on numerical simulation. Applied Mathematics and Mechanics (English Edition), 35(3), 277–284(2014) https://doi.org/10.1007/s10483-014-1790-8
[8] BECHTLE, S., HABELITZ, S., KLOCKE, A., FETT, T., and SCHNEIDER, G. A. The fracture behaviour of dental enamel. Biomaterials, 31(2), 375–384(2010)
[9] YANG, D., BHARATIYA, M., and GRINE, F. E. Hunter-Schreger band configuration in human molars reveals more decussation in the lateral enamel of ‘functional’ cusps than ‘guiding’ cusps. Archives of Oral Biology, 142, 105524(2022)
[10] MACHO, G. A., JIANG, Y., and SPEARS, I. R. Enamel microstructure — a truly threedimensional structure. Journal of Human Evolution, 45(1), 81–90(2003)
[11] BAIAJ, D. and AROLA, D. Role of prism decussation on fatigue crack growth and fracture of human enamel. Acta Biomaterialia, 5(8), 3045–3056(2009)
[12] ANG, S. F., BORTEL, E. L., SWAIN, M. V., KLOCKE, A., and SCHNEIDER, G. A. Sizedependent elastic/inelastic behavior of enamel over millimeter and nanometer length scales. Biomaterials, 31(7), 1955–1963(2010)
[13] BAIAJ, D., NAZARI, A., EIDELMAN, N., and AROLA, D. D. A comparison of fatigue crack growth in human enamel and hydroxyapatite. Biomaterials, 29(36), 4847–4854(2008)
[14] MYOUNG, S., LEE, J., CONSTANTINO, P., LUCAS, P., CHAI, H., and LAWN, B. Morphology and fracture of enamel. Journal of Biomechanics, 42(12), 1947–1951(2009)
[15] YILMAZ, E. D., SCHNEIDER, G. A., and SWAIN, M. V. Influence of structural hierarchy on the fracture behaviour of tooth enamel. Philosophical Transactions of the Royal Society A, 373, 20140130(2015)
[16] YAHYAZADEHFAR, M., BAJAJ, D., and AROLA, D. Hidden contribution of the enamel rods on the fracture resistance of human teeth. Acta Biomaterialia, 9(1), 4806–4814(2013)
[17] ÖZCOBAN, H., YILMAZ, E. D., and SCHNEIDER, G. A. Hierarchical microcrack model for materials exemplified at enamel. Dental Materials, 34(1), 69–77(2018)
[18] WILMERS, J. and BARGMANN, S. Nature’s design solutions in dental enamel: uniting high strength and extreme damage resistance. Acta Biomaterialia, 107, 1–24(2020)
[19] ANG, S. F., SCHULZ, A., FERNANDES, R. P., and SCHNEIDER, G. A. Sub-10-micrometer toughening and crack tip toughness of dental enamel. Journal of the Mechanical Behavior of Biomedical Materials, 4(3), 423–432(2011)
[20] WENG, Z. Y., LIU, Z. Q., RITCHIEB, R. O., JIAO, D., LI, D. S., WU, H. L., DENG, L. H., and ZHANG, Z. F. Giant panda’s tooth enamel: structure, mechanical behavior and toughening mechanisms under indentation. Journal of the Mechanical Behavior of Biomedical Materials, 64, 125–138(2016)
[21] PRO, J. W. and BARTHELAT, F. Discrete element models of fracture in tooth enamel: failure mode competition and statistical effects. Journal of the Mechanics and Physics of Solids, 137, 103868(2020)
[22] PRO, J. W. and BARTHELAT, F. Discrete element models of tooth enamel, a complex threedimensional biological composite. Acta Biomaterialia, 94, 536–552(2019)
[23] LIU, S., XU, Y., AN, B., and ZHANG, D. Interaction of rod decussation and crack growth in enamel. Computer Methods in Biomechanics and Biomedical Engineering, 11, 1–10(2022)
[24] ZHANG, N., WANG, X., XIANG, W., ZHONG, Y., YAN, F., and JIANG, B. Hierarchy structure and fracture mechanisms of the wild wolf tusk’s enamel. Materials Science & Engineering C, 106, 110277(2019)
[25] HE, L. H. and SWAIN, M. V. Understanding the mechanical behaviour of human enamel from its structural and compositional characteristics. Journal of the Mechanical Behavior of Biomedical Materials, 1(1), 18–29(2018)
[26] BARGMANN, S., SCHEIDER, I., XIAO, T., YILMAZ, E., SCHNEIDER, G. A., and HUBER, N. Towards bio-inspired engineering materials: modeling and simulation of the mechanical behavior of hierarchical bovine dental structure. Computational Materials Science, 79, 390–401(2013)
[27] 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)
[28] AN, B., WANG, R., and ZHANG, D. Role of crystal arrangement on the mechanical performance of enamel. Acta Biomaterialia, 8(10), 3784–3793(2012)
[29] YANG, W., SHERMAN, V. R., GLUDOVATZ, B., SCHAIBLE, E., STEWART, P., RITCHIE, R. O., and MEYERS, M. A. On the tear resistance of skin. Nature Communications, 6, 6649(2015)