Haversian cortical bone model with many radial microcracks: An elastic analytic solution

Najafi, Ahmad R.; Arshi, Ahmad Reza; Eslami, M. R.; Fariborz, S.J.; Moeinzadeh, Manssour H.

doi:10.1016/j.medengphy.2006.08.001

“…They used LEFM on a composite model of osteonal cortical bone and studied the osteonal effect on a microcrack oriented perpendicular to the external load. This study was later extended by Raeisi Najafi et al [95,163] to analyse the interaction of arbitrary microcracks in the vicinity of an osteon ( figure 7). In those studies, a two-dimensional fibrematrix composite material model assuming LEFM and a plane strain condition was used to represent a Haversian cortical bone.…”

Section: Models At the Microscale And Larger Scalesmentioning

confidence: 94%

“…The ageing process makes the interstitial bone tissue stiffer [39,92], which was shown numerically to have a profound effect on the bone fracture mechanics [74,[93][94][95][96][97]. In addition, ageing leads Bone toughness mechanisms at different levels of hierarchy.…”

Section: Bone Toughening Mechanismsmentioning

confidence: 99%

“…To solve the second problem, integral equations for the stress disturbance were obtained using an edge dislocation solution [164] as Green's function [165]. These studies showed the effect of microstructure morphology and heterogeneity on the fracture behaviour of cortical bone [95,97,163]. Their results also indicated that the mismatch between the material properties of the osteon and interstitial tissue governs fracture mechanisms: a soft osteon assists microcrack growth towards the osteon, while a stiff osteon repels the microcrack away from the osteon.…”

Section: Models At the Microscale And Larger Scalesmentioning

confidence: 99%

See 1 more Smart Citation

Modelling of bone fracture and strength at different length scales: a review

Sabet¹,

Najafi²,

Hamed³

et al. 2016

View full text Add to dashboard Cite

In this paper, we review analytical and computational models of bone fracture and strength. Bone fracture is a complex phenomenon due to the composite, inhomogeneous and hierarchical structure of bone. First, we briefly summarize the hierarchical structure of bone, spanning from the nanoscale, sub-microscale, microscale, mesoscale to the macroscale, and discuss experimental observations on failure mechanisms in bone at these scales. Then, we highlight representative analytical and computational models of bone fracture and strength at different length scales and discuss the main findings in the context of experiments. We conclude by summarizing the challenges in modelling of bone fracture and strength and list open topics for scientific exploration. Modelling of bone, accounting for different scales, provides new and needed insights into the fracture and strength of bone, which, in turn, can lead to improved diagnostic tools and treatments of bone diseases such as osteoporosis.

show abstract

“…Each model was meshed by 3-D, hexagonal and eight-node elements and same Poisson's ratio ν = 0.3) was determined for them [10,13,14] . Young's modulus calculated from test results was appointed to each model.…”

Section: Three-point Bending Testsmentioning

confidence: 99%

How Does The Bone Shaft Geometry Affect its Bending Properties?

Saffar¹

2009

American Journal of Applied Sciences

View full text Add to dashboard Cite

Abstract:In this research, ten fresh specimens of sheep tibiae were provided from slaughtered animals. Whole bone specimens were loaded in three-point bending according to standard wet bone test protocols. Mechanical properties were determined and compared with the results which were obtained from two dry bone tests. The results showed that fracture bending moment and bone extrinsic stiffness had significant relations with fracture cross-section dependent parameters (i.e., cross-section area and area moment of inertia). Where, fracture energy and ultimate strength did not have such a relation with these parameters. Finite element modeling of bone shaft was made with simplified geometry (neglecting cross-section variations along bone shaft) in two steps: First, by elliptical crosssection and second, by circular cross-section, assuming linear elastic and isotropic properties for the specimens. Elastic (Young's) modulus and fracture load, evaluated from curves obtained from tests, were applied to the finite element model and close results of maximum stress in both test specimen and first (elliptical cross-section) model showed up. There was an average difference of about 2% between ultimate strength of wet bone specimens and maximum (tensile) stress occurred in the elliptical models. However, this value for circular models was about 16%.

show abstract

“…Linear elastic and isotropic properties were considered for the models. Each model was meshed by 3-D, hexagonal and eight-node elements and same Poisson's ratio ν = 0.3) was determined for them [10,13,14] . Young's modulus calculated from test results was appointed to each model.…”

Section: Three-point Bending Testsmentioning

confidence: 99%

How Does The Bone Shaft Geometry Affect its Bending Properties?

Saffar¹,

Jamilpour²,

Rajaai³

2009

American J. of Applied Sciences

View full text Add to dashboard Cite

Abstract:In this research, ten fresh specimens of sheep tibiae were provided from slaughtered animals. Whole bone specimens were loaded in three-point bending according to standard wet bone test protocols. Mechanical properties were determined and compared with the results which were obtained from two dry bone tests. The results showed that fracture bending moment and bone extrinsic stiffness had significant relations with fracture cross-section dependent parameters (i.e., cross-section area and area moment of inertia). Where, fracture energy and ultimate strength did not have such a relation with these parameters. Finite element modeling of bone shaft was made with simplified geometry (neglecting cross-section variations along bone shaft) in two steps: First, by elliptical crosssection and second, by circular cross-section, assuming linear elastic and isotropic properties for the specimens. Elastic (Young's) modulus and fracture load, evaluated from curves obtained from tests, were applied to the finite element model and close results of maximum stress in both test specimen and first (elliptical cross-section) model showed up. There was an average difference of about 2% between ultimate strength of wet bone specimens and maximum (tensile) stress occurred in the elliptical models. However, this value for circular models was about 16%.

show abstract

Haversian cortical bone model with many radial microcracks: An elastic analytic solution

Cited by 29 publications

References 32 publications

Modelling of bone fracture and strength at different length scales: a review

Modelling of bone fracture and strength at different length scales: a review

How Does The Bone Shaft Geometry Affect its Bending Properties?

How Does The Bone Shaft Geometry Affect its Bending Properties?

Contact Info

Product

Resources

About