A structural mathematical model for the viscoelastic anisotropic behaviour of trabecular bone

Kafka, V.; Jìrová, Jitka

doi:10.3233/bir-1983-20607

Cited by 19 publications

(10 citation statements)

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“…The theory of hydraulic stiffening was originally developed for hard tissues (Kafka, 1993; Lowenhielm (1978) PBV NC NC Mohan and Melvin (1982) Aorta + NC Lee and Haut (1989) PBV NC NC Lee and Haut (1992) CA, JV NC NC Monson et al (2003) CBV NC NC À Present study Porcine aorta + À + PBV: parasagittal bridging vein; CA: carotid artery; JV: jugular vein; CBV: cerebral blood vessel; NC: no change; +: increase; À: decrease. Kafka and Jirova, 1983) but has also been applied to soft tissues (Haut and Haut, 1997). This theory explains increased stiffness under dynamic loading by considering viscous effects due to hydraulic pressure of hydrated soft tissues.…”

Section: Discussionmentioning

confidence: 98%

Mechanics of arterial subfailure with increasing loading rate

Stemper¹,

Yoganandan²,

Pintar³

2007

Journal of Biomechanics

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Section: Discussionmentioning

confidence: 98%

Mechanics of arterial subfailure with increasing loading rate

Stemper¹,

Yoganandan²,

Pintar³

2007

Journal of Biomechanics

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“…Under compression, the interstitial fluid flow and the inherent viscoelasticity of the solid matrix contribute to the apparent viscoelastic behavior of the trabecular bone (Biot 1962). For simplicity, Kafka and Jirova (1983) have described trabeculae as elastic behavior, and the viscous component with the Maxwell model. They showed that the viscous component must be taken into account in the modeling of the mechanical behavior of the trabecular bone, because under loading, one-third of the load is created by the viscous fluid.…”

Section: List Of Symbolsmentioning

confidence: 99%

A study of the viscoelastic effect in a bone remodeling model

Baïotto

Zidi

2008

Biomech Model Mechanobiol

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The present paper addresses the following question can a simple regulatory bone remodeling model predict effects of viscosity on the trabecular morphology? For that, we propose an extension of a previous bone remodeling model by taking into account the viscosity properties of the tissue. Zener's law is used to describe the mechanical behavior of the bone and a specific law of the apparent bone density rate is proposed. Based on stability analysis, numerical simulations are then performed to investigate the viscosity role on simulations of the bone remodeling process. We show that the viscous contribution affects the evolution of the apparent bone density, by slowing down the adaptation process, which seems to be confirmed by simulations with real data obtained from rat tibia.

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“…7,10,11,17,25,29,48,49 Several approaches have been used in these studies to formulate the basic poroelasticity equations, including RVE or effective medium theory (after Hashin and Shtrikman), 18 mixture theory, and two-space homogenization. The methods differ in the manner in which the microstructure and/or material properties are averaged or "homogenized."…”

Section: Constitutive Model For Strain-rate Dependent Bone Poroelastimentioning

confidence: 99%

“…The 2D-FE model was validated by computing the stress concentration factor (maximum tensile stress/applied stress) for a thin finite width plate with a circular hole, and comparing this result with the analytical solution. 25 We determined that a minimum of 3,000 triangular elements were necessary to obtain the analytical solution for the stress concentration factor at the edge of the hole and on the diameter perpendicular to the applied stress (maximum tensile stress/applied stress = 4.32 for a plate width to hole diameter ratio of 2).…”

Section: Bi-phasic Finite Element Modelmentioning

confidence: 99%

Hydraulic Strengthening Affects the Stiffness and Strength of Cortical Bone

Liebschner

Keller

2005

Ann Biomed Eng

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A nonlinear, interstitial fluid flow constitutive model for cortical bone was developed to study the strain-rate dependency of cortical bone apparent modulus (Ea). Nine representative volume element (RVE) structural models of cortical bone spanning an effective pore volume fraction P range of 1-40% were examined. Dynamic loading conditions were used to study the fluid flow contribution or hydraulic strengthening (HS) effect on Ea for each RVE model. The model indicated that there is an upper and lower asymptotic bound of strain-rate (10(+/-3) sec(-1)) above or below which there are no further HS effects on Ea. At certain strain-rates (10(-1) to 10(0) sec(-1)) variations in cortical bone porosity had little or no influence on Ea. At lower and higher frequencies, the loss tangent, hence the magnitude of viscoelastic effects is greater. For strain-rates less than 10(-1) sec(-1), lower porosity RVE models were always stiffer than higher porosity RVE models. A generalized power law model is proposed to account for the fact that HS in cortical bone exhibits an upper and lower asymptotic bound and is bi-modal in terms of strain-rate.

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A structural mathematical model for the viscoelastic anisotropic behaviour of trabecular bone

Cited by 19 publications

References 0 publications

Mechanics of arterial subfailure with increasing loading rate

Mechanics of arterial subfailure with increasing loading rate

A study of the viscoelastic effect in a bone remodeling model

Hydraulic Strengthening Affects the Stiffness and Strength of Cortical Bone

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