1998
DOI: 10.1023/a:1004303926771
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Cited by 82 publications
(10 citation statements)
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“…Previous attempts to model this anisotropy considered cylindrical osteons to be fibers embedded in a less stiff matrix, [8] a picture which is unlikely to be true given the observed higher stiffness of the older interstitial bone. [4] Later models assess the anisotropy of the elastic modulus as a function of a platelet-like structural array within a collagenous matrix, [9,10] leading to slightly higher absolute values with an anisotropy ratio of 1:2, which is higher but not too different from the nanoindentation (NI) data presented here. Microhardness measurements also showed a decrease in hardness of fibrils indented perpendicularly to their longitudinal bone axis relative to fibrils indented along their axis.…”
Section: Introductionmentioning
confidence: 57%
“…Previous attempts to model this anisotropy considered cylindrical osteons to be fibers embedded in a less stiff matrix, [8] a picture which is unlikely to be true given the observed higher stiffness of the older interstitial bone. [4] Later models assess the anisotropy of the elastic modulus as a function of a platelet-like structural array within a collagenous matrix, [9,10] leading to slightly higher absolute values with an anisotropy ratio of 1:2, which is higher but not too different from the nanoindentation (NI) data presented here. Microhardness measurements also showed a decrease in hardness of fibrils indented perpendicularly to their longitudinal bone axis relative to fibrils indented along their axis.…”
Section: Introductionmentioning
confidence: 57%
“…The smallest experimental characteristic length probed (50 nm maximum depth, approximately 400 nm contact diameter) is comparable to the size of a few mineralized collagen fibrils and allowed the evaluation of the mechanical properties of a single sub-layer of fibrils in the lamellar structure; whereas, the largest experimental characteristic length sampled (300 nm maximum depth, approx. 2 mm contact diameter) may accommodate approximately 10-20 bunches of collagen fibrils oriented along multiple directions and, thus, involves multiple sub-layers, whose thickness can vary between few hundreds of nanometres to a couple of microns [22,[33][34][35]. These investigations enabled the identification of a decrease in the values of indentation moduli with the penetration depth (figure 5a) that indicates a possible size effect in the mechanical properties of cortical bone tissue.…”
Section: Discussionmentioning
confidence: 99%
“…Although various models have been proposed by different groups to calculate the tissue modulus, these models invariably correlated the modulus and the hierarchical levels of the materials. The longitudinal modulus can be calculated according to the HalpinTsai model [ 70 ] :…”
Section: Relationship Of Hierarchical Structures and Deformation Mechmentioning
confidence: 99%