Elastic properties of apatites

Gilmore, R. S.; Katz, J. Lawrence

doi:10.1007/bf00543533

Cited by 192 publications

(99 citation statements)

References 14 publications

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“…Tests with an ultrasonic interferometer coupled with a solid media pressure apparatus Ukraincik, 1971, Gilmore andKatz, 1982] reveal the isotropic elastic properties of hydroxyapatite powder (Table 1), which, in view of the largely disordered arrangement of poorly crystalline minerals [Lees et al, 1994, Fratzl et al, 1996, Peters et al, 2000, Epple, 2001, Hellmich and Ulm, 2002a, 2003, Hellmich et al, 2004a, are sufficient for the characterization of the mineral phase [Hellmich and Ulm, 2002b, Hellmich et al, 2004b, Fritsch et al, 2006. Given the absence of direct measurements of (molecular) collagen, the elastic properties of (molecular) collagen are approximated by those of dry rat tail tendon, a tissue consisting almost exclusively of collagen.…”

Section: Elastic Properties Of Hydroxyapatite Collagen and Watermentioning

confidence: 99%

Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength

Fritsch

Hellmich

Dormieux

2009

Journal of Theoretical Biology

176

128

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To cite this version:Andreas Fritsch, Christian Hellmich, Luc Dormieux.Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength. Journal of Theoretical Biology, Elsevier, 2009, 260 (2) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A c c e p t e d m a n u s c r i p t AbstractThere is an ongoing discussion on how bone strength could be explained from its internal structure and composition. Reviewing recent experimental and molecular dynamics studies, we here propose a new vision on bone material failure: mutual ductile sliding of hydroxyapatite mineral crystals along layered water films is followed by rupture of collagen crosslinks. In order to cast this vision into a mathematical form, a multiscale continuum micromechanics theory for upscaling of elastoplastic properties is developed, based on the concept of concentration and influence tensors for eigenstressed microheterogeneous materials. The model reflects bone's hierarchical organization, in terms of representative volume elements for cortical bone, for extravascular and extracellular bone material, for mineralized fibrils and the extrafibrillar space, and for wet collagen. In order to get access to the stress states at the interfaces between crystals, the extrafibrillar mineral is resolved into an infinite amount of cylindrical material phases oriented in all directions in space. The multiscale micromechanics model is shown to be able to satisfactorily predict the strength characteristics of different bones from different species, on the basis of their mineral/collagen content, their intercrystalline, intermolecular, lacunar, and vascular porosities, and the elastic and strength properties of hydroxyapatite and (molecular) collagen. Preprint submitted to Journal of Theoretical Biology 6 May 2009A c c e p t e d m a n u s c r i p t

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Section: Elastic Properties Of Hydroxyapatite Collagen and Watermentioning

confidence: 99%

Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength

Fritsch

Hellmich

Dormieux

2009

Journal of Theoretical Biology

176

128

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“…An early review of some of the mechanical and physical properties of teeth through 1979 [92] summarizes the state-of-the-art prior to the development of modern microand nanotechniques of measuring tissue properties. Bulk acoustic wave propagation techniques were used to measure the properties of dental materials in a number of studies by Katz and his colleagues and students: dentin and enamel [91], amalgams [93][94][95], cements [96], composites [97][98][99], alloys [100] and anticipating tissue engineering based on apatites, a series of studies of various synthetic and biological apatites [101][102][103]. The availability of such detailed data on properties has also allowed the development of various models to explain and/or predict the properties both of natural [104] and synthetic biomaterials [105][106][107].…”

Section: Mechanical Analysis With Ultrasonic Wave Propagation Techniquesmentioning

confidence: 99%

Multiscale mechanics of hierarchical structure/property relationships in calcified tissues and tissue/material interfaces

Katz

Misra

Spencer

et al. 2007

Materials Science and Engineering: C

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This paper presents a review plus new data that describes the role hierarchical nanostructural properties play in developing an understanding of the effect of scale on the material properties (chemical, elastic and electrical) of calcified tissues as well as the interfaces that form between such tissues and biomaterials. Both nanostructural and microstructural properties will be considered starting with the size and shape of the apatitic mineralites in both young and mature bovine bone. Microstructural properties for human dentin and cortical and trabecular bone will be considered. These separate sets of data will be combined mathematically to advance the effects of scale on the modeling of these tissues and the tissue/biomaterial interfaces as hierarchical material/structural composites. Interfacial structure and properties to be considered in greatest detail will be that of the dentin/adhesive (d/a) interface, which presents a clear example of examining all three material properties, (chemical, elastic and electrical). In this case, finite element modeling (FEA) was based on the actual measured values of the structure and elastic properties of the materials comprising the d/a interface; this combination provides insight into factors and mechanisms that contribute to premature failure of dental composite fillings. At present, there are more elastic property data obtained by microstructural measurements, especially high frequency ultrasonic wave propagation (UWP) and scanning acoustic microscopy (SAM) techniques. However, atomic force microscopy (AFM) and nanoindentation (NI) of cortical and trabecular bone and the dentin-enamel junction (DEJ) among others have become available allowing correlation of the nanostructural level measurements with those made on the microstructural level.

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“…The joints in the bone structure consist of a mineral hydroxyapatite component shown to exhibit elastoplastic behaviour (9,14,15,24,25).…”

Section: Structural Analysis Of Bonesmentioning

confidence: 99%

Constitutive Laws and Failure Models for Compact Bones Subjected to Dynamic Loading

Pithioux

Chabrand

Jean

2002

Computer Methods in Biomechanics and Biomedical Engineering

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ABSTRACT:Many biological tissues, such as bones and ligaments, are fibrous. The geometrical structure of these tissues shows that they exhibit a similar hierarchy in their ultra-structure and macro-structure. The aim of this work is to develop a model to study the failure of fibrous structures subjected to dynamic loading. The important feature of this model is that it describes failure in terms of the loss of cohesion between fibres. We have developed a model based on the lamellar structure of compact bone with fibres oriented at 0°, 45° and 90° to the longitudinal axis of the bone, and have studied the influence of the model parameters on the failure process. Bone porosity and joint stress force at failure were found to be the most significant parameters. Using least square resolution, we deduced a phenomenological model of the lamellar structure. Finally, experimental results were found to be comparable with our numerical model.

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Elastic properties of apatites

Cited by 192 publications

References 14 publications

Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength

Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength

Multiscale mechanics of hierarchical structure/property relationships in calcified tissues and tissue/material interfaces

Constitutive Laws and Failure Models for Compact Bones Subjected to Dynamic Loading

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