An elastic compound tube model for a single osteon

Braidotti, P; Branca, F. P.; Sciubba, Enrico; Stagni, Luigi

doi:10.1016/0021-9290(94)00082-f

Cited by 17 publications

(10 citation statements)

References 8 publications

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“…These pushout data suggest that the highest values of maximum interfacial shear stress is in the proximal diaphysis while those in the mid to distal diaphyses are lower. Osteon spatial orientation is heavily influenced by magnitudes of torsion and bending moments (Braidotti et al, 1995). These influences may not only contribute to spatial orientation, but also to changes in the area fraction of osteons as well as changes in osteon interfacial properties resulting in decreased maximum interfacial shear stress within the mid to distal diaphyses.…”

Section: Article In Pressmentioning

confidence: 99%

“…This could result from a varied osteonal structure, the number of lamellae making up the osteon, the degree of mineralization, or a combination of all these factors. Osteon structure has been modeled in a detailed form, and it has been predicted that Poisson's ratio is affected (Braidotti et al, 1995). If Poisson's ratio of the osteon is related to structure (implicitly the osteon type) then the forces necessary to cause debonding, frictional sliding or other phenomena associated with the interface may be altered.…”

Section: Article In Pressmentioning

confidence: 99%

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Osteon interfacial strength and histomorphometry of equine cortical bone

Bigley

Griffin

Christensen

et al. 2006

Journal of Biomechanics

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The interfacial strength of secondary osteons from the diaphysis of the Thoroughbred equine third metacarpal was evaluated using the fiber pushout test. The pushout was performed on 300-500 microm sections of 4x4x15 mm bone blocks machined from four anatomic regions of the cortex. Pushout strength was evaluated from proximal to distal location within the diaphysis on four osteon types classified under polarized light on adjacent histologic sections from each block. The shear strength of the interfaces were estimated from shear lag theory. Differences were found in the interfacial strength of osteons based on appearance under polarized light with bright field having the highest interfacial strength (40.3 MPa). The lowest strength was found in the dark field osteons (22.8 MPa). The dorsal region had the highest shear strength and toughness compared to all other regions. The cement line and interlamellar interfaces are similar in strength, but exhibit regional dependence--specifically, the palmar region strength is less (17.5 MPa) than the osteon interlamellar interfaces (30.4 MPa) and osteon type dependent (alternating significantly weaker than other types). Histomorphometry revealed significant regional differences (p<0.0001) in osteon area fraction among the four osteon types as well as differences in the osteon diameter (p=0.01), with dorsal regions having larger osteons (170 microm) than the palmar region (151 microm). Fatigue life and fracture toughness of Haversian bone are reported in the literature to be regionally dependent and are known to be associated with osteon pullout--an osteon interfacial phenomenon. Therefore, the results presented in this study are important to further the understanding of the mechanisms of fragility and damage accumulation in cortical bone.

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Section: Article In Pressmentioning

confidence: 99%

Section: Article In Pressmentioning

confidence: 99%

Osteon interfacial strength and histomorphometry of equine cortical bone

Bigley

Griffin

Christensen

et al. 2006

Journal of Biomechanics

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“…Hellmich et al 18 showed that the interplay between pore pressure and skeleton deformation depends strongly on the loading direction and on the characteristic size of the pores. Braidotti et al 19 and Stagni 20,21 proposed analytical models of a single osteon. The linear elastic multilayered tube model under tension with initial stresses was established by Braidotti et al 19 They noticed that exchanging the material constants of odd and even layers produced a great effect on intrinsic energy.…”

Section: Introductionmentioning

confidence: 99%

“…Braidotti et al 19 and Stagni 20,21 proposed analytical models of a single osteon. The linear elastic multilayered tube model under tension with initial stresses was established by Braidotti et al 19 They noticed that exchanging the material constants of odd and even layers produced a great effect on intrinsic energy. Stagni 20 treated the problem of a laminated inclusion with eigenstrains, under remote loading as the plane elasticity state and presented the solution based on the complex variable method.…”

Section: Introductionmentioning

confidence: 99%

Effects of geometry and loading on the elastic behavior of a single osteon via analytical structural mechanics approaches

Asadollahi

Dehestani

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this study, two analytical approaches for lamella texture at micro-scale including disordered mineralized and organized collagen fibers are employed to provide analytical models of an osteon. A two-step homogenization procedure is also applied to characterize the elastic properties of the osteon. Numerical evaluations are accomplished to explore the effects of loading and geometrical parameters on the behavior of the osteon. Results show the diameter of the Haversian canal is the dominant geometrical parameter influencing the elastic stresses in the osteon. The radial and hoop stresses as well as radial displacement are insensitive to the changes in the number of lamellae. The ordered motif osteon model can also be used to explain circumferential micro-cracks along lamellae leading to irregular profiles of fracture in osteon direct tensile tests. The theoretical model of osteon based on the lamination theory generally indicated better agreement with existing experimental results.

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“…Heterogeneous materials may be modelled using multiscale modelling, which represents the global behaviour of a heterogeneous material by firstly developing a representative volume element that incorporates microstructural detail at the scale of interest . After applying homogeneous boundary conditions the mechanical response of the representative volume element can then be used to identify the constitutive parameters in homogenized, Cauchy‐type continuum representations of the material.…”

Section: Introductionmentioning

confidence: 99%

A numerical investigation and experimental verification of size effects in loaded bovine cortical bone

Frame

Wheel

Riches

2017

Numer Methods Biomed Eng

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In this paper, we present 2-and 3-dimensional finite element-based numerical models of loaded bovine cortical bone that explicitly incorporate the dominant microstructural feature: the vascular channel or Haversian canal system. The finite element models along with the representation of the microstructure within them are relatively simple: 2-dimensional models, consisting of a structured mesh of linear elastic planar elements punctuated by a periodic distribution of circular voids, are used to represent beam samples of cortical bone in which the channels are orientated perpendicular to the sample major axis, while 3-dimensional models, using a corresponding mesh of equivalent solid elements, represent those samples in which the canals are aligned with the axis. However, these models are exploited in an entirely novel approach involving the representation of material samples of different sizes and surface morphology. The numerical results obtained for the virtual material samples when loaded in bending indicate that they exhibit size effects not forecast by either classical (Cauchy) or more generalized elasticity theories. However, these effects are qualitatively consistent with those that we observed in a series of carefully conducted experiments involving the flexural testing of bone samples of different sizes. Encouraged by this qualitative agreement, we have identified appropriate model parameters, primarily void volume fraction but also void separation and matrix modulus by matching the computed size effects to those we observed experimentally. Interestingly, the parameter choices that provide the most suitable match of these effects broadly concur with those we actually observed in cortical bone.KEYWORDS cortical bone, finite element analysis, generalized continuum, mechanical behaviour, micropolar (Cosserat) elasticity, size effect

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An elastic compound tube model for a single osteon

Cited by 17 publications

References 8 publications

Osteon interfacial strength and histomorphometry of equine cortical bone

Osteon interfacial strength and histomorphometry of equine cortical bone

Effects of geometry and loading on the elastic behavior of a single osteon via analytical structural mechanics approaches

A numerical investigation and experimental verification of size effects in loaded bovine cortical bone

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