The mechanics of three-dimensional cellular materials

Gibson, Lorna; Ashby, Michael F.

doi:10.1098/rspa.1982.0088

Cited by 1,060 publications

(411 citation statements)

References 11 publications

(9 reference statements)

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“…The value of the empirically determined exponent depends on the geometrical structure of the solid matrix, and lies within the range of to about 4, where holds for any straight tubular pores (honeycomb structures), for homogenous and isotropic cellular open-cell foams (such as aluminium foal), and for close-cell foams (Scheffler and Colombo 2005;Ashby 1983;Gibson and Ashby 1982). In this study the value of the exponent is set to be 2.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Application of Acoustic Bessel Beams for Handling of Hollow Porous Spheres

Azarpeyvand

2014

Ultrasound in Medicine & Biology

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ABSTRACT-Acoustic manipulation of porous spherical shells, widely used as drug delivery carriers and magnetic resonance imaging contrast agents, is investigated analytically. The technique used for this purpose is based on the application of high-order Bessel beams for as a single-beam acoustic manipulation device, using which particles lying on the axis of the beam can be pulled toward the beam source. The exerted acoustic radiation force is calculated using the standard partial-wave series method and the wave propagation within the porous media is modeled using Biot's theory of poroelasticity. Numerical simulations are performed for porous aluminum and silica shells of different thicknesses and porosities.Results have shown that manipulation of low-porosity shells is possible using Bessel beams with large conical angles, over a number of broadband frequency ranges; while that for highly porous shells generally occurs over some narrowband frequency domains at much smaller conical angles.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Application of Acoustic Bessel Beams for Handling of Hollow Porous Spheres

Azarpeyvand

2014

Ultrasound in Medicine & Biology

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“…Standard mechanics approaches approximate either the apparent strain, sapp, by displacement boundary conditions (Christenson, 1986;Beaupre and Hayes, 1985;Iremonger and Lawler, 1980;Hill, 1963;Hashin, 1962), or the apparent stress, u.,,,,, by traction boundary conditions (Gibson and Ashby, 1988;Huber and Gibson, 1988;Gibson and Ashby, 1982;Kanakkanatt, 1973;Pate1 and Finnie, 1970;Ko, 1965;Gent and Thomas, 1959). These approaches then solve for the total tissue strain using the assumed boundary conditions.…”

Section: The Best Fits Between Predicted and Experimentalmentioning

confidence: 99%

“…Standard mechanics approaches, which have been applied to analyze composite materials (Hill, 1963;Hashin, 1962;reviewed by Hashin, 1983) and cellular foams (Gibson and Ashby, 1988;Huber and Gibson, 1988;Christenson, 1986;Gibson and Ashby, 1982;Iremonger and Lawler, 1980;Kanakkanatt, 1973;Lederman, 1971;Pate1 and Finnie, 1970;Ko, 1965;Gent and Thomas, 1959) as well as trabecular bone (Beaupre and Hayes, 1985;Gibson and Ashby, 1988;t Suquet (1985) denotes the tensor equivalent of CM] as the strain localization tensor. 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.…”

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, many researchers have extensively studied the fundamental aspects of cork's mechanical behavior under quasi-static axial compressive loading [20][21][22][23][24][25][26][27]. More recently, and regarding agglomerated cork (details on how agglomerated cork is produced can be found in [28]), the influence of cork density on cork's mechanical behavior under compression, as well as the subsequent recovery of dimensions were studied by Anjos et al [29].…”

Section: Contents Lists Available At Sciencedirectmentioning

confidence: 99%

Comparing the mechanical performance of synthetic and natural cellular materials

et al. 2015

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a b s t r a c tThis work compares the mechanical performance of agglomerated cork against synthetic materials typically used as impact energy absorbers. Particularly, the study will focus on the expanded polystyrene (EPS) and expanded polypropylene (EPP).Firstly, quasi-static compression tests are performed in order to assess the energy storage capacity and to characterize the stress-strain behavior cellular materials under study. Secondly, guided drop tests are performed to study the response of these materials when subjected to multiple dynamic loading (two impacts). Thirdly, finite element analysis (FEA) is carried out in order to simulate the compressive behavior of the studied materials under dynamic loading.Results show that agglomerated cork is an excellent alternative to the synthetic materials. Not only for being a natural and sustainable material but also for withstanding considerable impact energies. In addition, its capacity to keep some of its initial properties after loading (regarding mechanical properties and dimensions) makes this material highly desirable for multiple-impact applications.

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The mechanics of three-dimensional cellular materials

Abstract: The mechanical properties (the moduli and collapse strengths) of three dimensional cellular solids or foams are related to the properties of the cell wall, and to the cell geometry. The results of the analyses give a good description of a large body of data for polymeric foams.

Cited by 1,060 publications

References 11 publications

Application of Acoustic Bessel Beams for Handling of Hollow Porous Spheres

Application of Acoustic Bessel Beams for Handling of Hollow Porous Spheres

Application of homogenization theory to the study of trabecular bone mechanics

Comparing the mechanical performance of synthetic and natural cellular materials

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