Properties and an Anisotropic Model of Cancellous Bone From the Proximal Tibial Epiphysis

Williams, J. L.; Lewis, Jack L.

doi:10.1115/1.3138303

Cited by 360 publications

(133 citation statements)

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“…Trabecular bone has an aligned composite porous micro structure and is both inhomogeneous and anisotropic (Townsend et al, 1975;Williams and Lewis, 1982;Hodgskinson and Currey, 1990). Solely on-axis uniaxial and confined compression testing was performed for BTB therefore the anisotropy of the trabecular specimens could not be determined.…”

Section: Discussionmentioning

confidence: 99%

Experimental and numerical characterisation of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue

Kelly

McGarry

2012

Journal of the Mechanical Behavior of Biomedical Materials

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Section: Discussionmentioning

confidence: 99%

Experimental and numerical characterisation of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue

Kelly

McGarry

2012

Journal of the Mechanical Behavior of Biomedical Materials

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“…Pugh et al (1973) modeled the subchondral trabecular bone as a collection of structural plates and concluded that bending and buckling were major modes of deformation of the trabeculae. Williams and Lewis (1982) modeled the exact structure of a twodimensional section of trabecular bone with plane strain finite elements to predict the apparent transversely isotropic elastic constants. They concluded that the modulus of trabecular bone tissue was much less than that of cortical bone tissue.…”

Section: Introductionmentioning

confidence: 99%

“…Gibson, 1985;Williams and Lewis, 1982;Pugh et al, 1973), generally assume that the effect of the apparent stress, {Q,,,} (or strain, {E,~~}) on the microstructure can be represented by self equilibrated anti-periodic traction or displacement boundary conditions. These approaches then solve for the total tissue strain using the standard form of the variational equilibrium equation (shown here for the traction boundary condition):…”

Section: Introductionmentioning

confidence: 99%

Application of homogenization theory to the study of trabecular bone mechanics

Hollister

Fyhrie

Jepsen

et al. 1991

Journal of Biomechanics

137

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Ah&act-It is generally accepted that the strength and stiffness of trabecular bone is strongly affected by trabecular microstructure. It has also been hvoothesized that stress induced adaptation of trabecular bone is affected by trabecular tissue level stress and;& strain. At this time, however, there is no generally accepted (or easily accomplished) technique for predicting the effect of microstructure on trabecular bone apparent stiffness and strength or estimating tissue level stress or strain. In this paper, a recently developed mechanics theory specifically designed to analyze microstructured materials, called the homogenization theory, is presented and applied to analyze trabecular bone mechanics. Using the homogenization theory it is possible to perform microstructural and continuum analyses separately and then combine them in a systematic manner. Stiffness predictions from two different microstructural models of trabecular bone show reasonable agreement with experimental results, depending on metaphyseal region, (R">0.5 for proximai humerus specimens, R* ~0.5 for distal femur and proximal tibia specimens). Estimates of both microstructural strain energy density (SED) and apparent SED show that there are large differences (up to 30 times) between apparent SED (as calculated by standard continuum finite element analyses) and the maximum microstructural or tissue SED. Furthermore, a strut and spherical void microstructure gave very different estimates of maximum tissue SED for the same bone volume fraction (BV/TV). The estimates from the spherical void microstructure are between 2 and 20 times greater than the strut microstructure at lo-20% W/TV INTRODUCTION Stress and strain fields in individual trabeculae are determined by both overall metaphyseal geometry and the microstructural organization of a local region of trabeculae. However, directly calculating stress and strain fields for each trabecula of a whole metaphysis is impossible with current computational technology. Current techniques for determining trabecular stress have focused on either analyzing very small regions of bone with a limited number of trabeculae, or analyzing a much larger region of bone assuming it to be a solid with apparent material properties. Neither technique provides direct information about trabecular tissue stresses and strains in an entire metaphyseal region. The homogenization theory is a recently developed method which provides a systematic way to combine stress analyses at the metaphyseal and individual trabecula level. This paper presents the initial application of homogenization theory to the study of trabecular bone mechanics.Microstructural analyses are generally used to predict apparent moduli and stress distributions within representative pieces of a given microstructure. These analyses assume that the whole microstructure within a material is constructed by repeating the representative piece analyzed. This type of analysis is quite Received infinalform 14 February 1991.

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“…However, natural auxetic materials do exist, examples being single crystals of arsenic (35) and cadmium (36), α-cristobalite (37), and many cubic elemental metals (38). In addition, some biological materials have been found to be auxetic, including certain forms of skin, for example, cat skin (39), salamander skin (40), and cow teat skin (41), and load-bearing cancellous bone from human shins (42). Furthermore, the mechanisms of auxetic materials depend on either their microstructure or their geometrical structure and on the deformation mechanisms of these structures when they deform.…”

Section: Introductionmentioning

confidence: 99%

Three decades of auxetic polymers: a review

Bhullar

2015

E-Polymers

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Developments in design and technology in the engineering and medical fields necessitate the use of smart and high-performance materials to meet higher engineering specifications. The general requirements of such materials include a combination of high stiffness and strength with significant weight savings, resistance to corrosion, chemical resistance, low maintenance, and reduced costs. Over the last three decades, it has been demonstrated that auxetic materials offer a huge potential for the fields of engineering, natural sciences, and biomedical engineering, and for many other industries, including the aerospace and defense industries, through their unique deformation mechanism and measured enhancements in mechanical properties. To meet future engineering challenges, auxetic materials are increasingly being recognized as integral components of smart and advanced materials. Although materials with a negative Poisson's ratio have been known since the early 1900s, they did not capture researchers' attention until the late 1980s. Since 1991, these materials have been known as auxetic materials. Since then, their benefits and applications have been expanded to all major classes of materials such as metals, ceramics, polymers, and composites, and they are also now being used in engineering applications. The goal of this review was to present the development of auxetic polymers, which were first fabricated in the form of polyurethane foam approximately three decades ago and are now used in the fabrication of non-woven nano/ micropolymeric structures. This review could provide useful information for the future development of auxetic polymers.

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Properties and an Anisotropic Model of Cancellous Bone From the Proximal Tibial Epiphysis

Cited by 360 publications

References 0 publications

Experimental and numerical characterisation of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue

Experimental and numerical characterisation of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue

Application of homogenization theory to the study of trabecular bone mechanics

Three decades of auxetic polymers: a review

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