{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T18:41:56Z","timestamp":1785436916073,"version":"3.56.0"},"reference-count":36,"publisher":"ASME International","issue":"12","license":[{"start":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T00:00:00Z","timestamp":1725580800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.asme.org\/publications-submissions\/publishing-information\/legal-policies"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12072187"],"award-info":[{"award-number":["12072187"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Dentin is a biological composite exhibiting multilevel hierarchical structure, which confers excellent damage tolerance to this tissue. Despite the progress in characterization of fracture behavior of dentin, the contribution of composite structure consisting of peritubular dentin (PTD), intertubular dentin (ITD) and tubules to fracture resistance remains elusive. In this study, calculations are carried out for energy release rate associated with crack propagation in the microstructure of dentin. Crack penetration and deflection at the PTD\u2013ITD interface are accounted for in the numerical analyses. It is found that high stiffness of the PTD plays a role in increasing crack driving force, promoting crack growth in the microstructure of dentin. For crack penetration across the PTD\u2013ITD interface, the crack driving force increases with increasing tubule radius; and thick PTD generates amplified crack driving force, thereby leading to weak fracture resistance. The driving force for crack deflection increases with the increase in tubule radius in the case of short cracks, while for long cracks, there is a decrease in driving force with increasing tubule radius. Furthermore, we show that the competition between crack penetration and deflection at the PTD-ITD interface is controlled by the ratio of PTD to ITD elastic modulus, tubule radius and thickness of PTD. High PTD stiffness can increase the propensity of crack deflection. The microstructure of dentin with large tubule radius favors crack deflection and thick PTD is beneficial for crack penetration.<\/jats:p>","DOI":"10.1115\/1.4066286","type":"journal-article","created":{"date-parts":[[2024,8,21]],"date-time":"2024-08-21T23:32:15Z","timestamp":1724283135000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":0,"title":["A Numerical Study of Crack Penetration and Deflection at the Interface Between Peritubular and Intertubular Dentin"],"prefix":"10.1115","volume":"146","author":[{"given":"Min","family":"Xu","sequence":"first","affiliation":[{"name":"Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University , Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhangying","family":"Xu","sequence":"additional","affiliation":[{"name":"QianWeiChang College, Shanghai University , Shanghai 200444, China"},{"id":[{"id":"https:\/\/ror.org\/006teas31","id-type":"ROR","asserted-by":"publisher"}],"name":"Shanghai University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bingbing","family":"An","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University , Shanghai 200444, China ; , Shaoxing 312074, China ; , Zhangwu Road, Shanghai 200092, China"},{"name":"Shaoxing Institute of Technology, Shanghai University , Shanghai 200444, China ; , Shaoxing 312074, China ; , Zhangwu Road, Shanghai 200092, China"},{"name":"Shanghai Institute of Aircraft Mechanics and Control , Shanghai 200444, China ; , Shaoxing 312074, China ; , Zhangwu Road, Shanghai 200092, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"33","published-online":{"date-parts":[[2024,9,6]]},"reference":[{"issue":"6","key":"2024090614142798500_bib1","doi-asserted-by":"crossref","first-page":"2172","DOI":"10.1016\/j.actbio.2009.11.017","article-title":"Synchrotron X-Ray Diffraction Study of Load Partitioning During Elastic Deformation of Bovine Dentin","volume":"6","year":"2010","journal-title":"Acta Biomater."},{"key":"2024090614142798500_bib2","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.jmbbm.2012.03.007","article-title":"Enamel and Dentin as Multi-Scale Bio-Composites","volume":"12","year":"2012","journal-title":"J. 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