2017
DOI: 10.1007/s10237-017-0971-x
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Explicit expressions for the estimation of the elastic constants of lamellar bone as a function of the volumetric mineral content using a multi-scale approach

Abstract: In this work, explicit expressions to estimate all the transversely isotropic elastic constants of lamellar bone as a function of the volumetric bone mineral density (BMD) are provided. The methodology presented is based on the direct homogenization procedure using the finite element method, the continuum approach based on the Hill bounds, the least-square method and the mean field technique. Firstly, a detailed description of the volumetric content of the different components of bone is provided. The paramete… Show more

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Cited by 10 publications
(8 citation statements)
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“…The mechanical properties of the sublamellae and the interstitial matrix are listed in Table S1, Supporting Information. The interstitial matrix, instead, is simplified as isotropic because it is not characterized by a specific and regular pattern as the osteon . To properly study the radial distribution of the stresses, all the models have at least three elements in the thickness of each sublamella.…”
Section: Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…The mechanical properties of the sublamellae and the interstitial matrix are listed in Table S1, Supporting Information. The interstitial matrix, instead, is simplified as isotropic because it is not characterized by a specific and regular pattern as the osteon . To properly study the radial distribution of the stresses, all the models have at least three elements in the thickness of each sublamella.…”
Section: Methodsmentioning
confidence: 99%
“…The interstitial matrix, instead, is simplified as isotropic because it is not characterized by a specific and regular pattern as the osteon. [28] To properly study the radial distribution of the stresses, all the models have at least three elements in the thickness of each sublamella. All the models have 8-node linear brick elements with reduced integration and hourglass control (C3D8R).…”
Section: Prsmentioning
confidence: 99%
“…The starting point of the current numerical model is considering the equations for estimating the elastic constants of a healthy bone as a function of the trabecular bone mineral density (BMD) in a multiscale approach [14]. Vercher et al [14] assumed the lamellar tissue as a transversely isotropic material (Figure 2a). The elastic constants of the lamellar bone are given in [14].…”
Section: Modelling Porosity In Lamellar Tissuementioning
confidence: 99%
“…Vercher et al [14] assumed the lamellar tissue as a transversely isotropic material (Figure 2a). The elastic constants of the lamellar bone are given in [14].…”
Section: Modelling Porosity In Lamellar Tissuementioning
confidence: 99%
“…The interstitial matrix instead, is simplified as isotropic, since it is not characterized by a specific and regular pattern as the osteon. [28] To properly study the radial distribution of the stresses, all the models have at least three elements in the thickness of each sub-lamella. All the models have 8-node linear brick elements with reduced integration and hourglass control (C3D8R).…”
Section: Author Manuscriptmentioning
confidence: 99%