Composites with Inclusions of Negative Bulk Modulus: Extreme Damping and                 Negative Poisson’s Ratio

Wang, Yun-Che; Lakes, Roderic S.

doi:10.1177/0021998305051112

Cited by 99 publications

(67 citation statements)

References 35 publications

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“…We increased and decreased each material parameter by 10 % of its baseline value while keeping all other parameters at their baseline values. For all stable isotropic elastic materials, the Poisson's ratio has a finite range, from −1 for completely compressible materials to 0.5 for completely incompressible materials (e.g., Wang and Lakes 2005;Greaves et al 2011). This is in contrast with the Young's modulus, density and thickness, which in principle can range from zero to infinity.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Finite-Element Modelling of the Response of the Gerbil Middle Ear to Sound

Maftoon

Funnell

Daniel

et al. 2015

JARO

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We present a finite-element model of the gerbil middle ear that, using a set of baseline parameters based primarily on a priori estimates from the literature, generates responses that are comparable with responses we measured in vivo using multi-point vibrometry and with those measured by other groups. We investigated the similarity of numerous features (umbo, pars-flaccida and pars-tensa displacement magnitudes, the resonance frequency and break-up frequency, etc.) in the experimental responses with corresponding ones in the model responses, as opposed to simply computing frequency-by-frequency differences between experimental and model responses. The umbo response of the model is within the range of variability seen in the experimental data in terms of the low-frequency (i.e., well below the middle-ear resonance) magnitude and phase, the main resonance frequency and magnitude, and the roll-off slope and irregularities in the response above the resonance frequency, but is somewhat high for frequencies above the resonance frequency. At low frequencies, the ossicular axis of rotation of the model appears to correspond to the anatomical axis but the behaviour is more complex at high frequencies (i.e., above the pars-tensa break-up). The behaviour of the pars tensa in the model is similar to what is observed experimentally in terms of magnitudes, phases, the break-up frequency of the spatial vibration pattern, and the bandwidths of the high-frequency response features. A sensitivity analysis showed that the parameters that have the strongest effects on the model results are the Young's modulus, thickness and density of the pars tensa; the Young's modulus of the stapedial annular ligament; and the Young's modulus and density of the malleus. Displacements of the tympanic membrane and manubrium and the lowfrequency displacement of the stapes did not show large changes when the material properties of the incus, stapes, incudomallear joint, incudostapedial joint, and posterior incudal ligament were changed by ±10 % from their values in the baseline parameter set.

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Section: Sensitivity Analysismentioning

confidence: 99%

Finite-Element Modelling of the Response of the Gerbil Middle Ear to Sound

Maftoon

Funnell

Daniel

et al. 2015

JARO

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“…9 Especially, when a structure with a volumeshrinking effect is used as an inclusion in a composite structure, a series of special material properties could be achieved. 10,11 One of the seminal studies is the Lakes's theoretical analysis of a conceptual composite with extreme damping and a negative Poisson's ratio (NPR). 10 In his study, a concept of a composite system with perfect inclusions 10 is…”

Section: Introductionmentioning

confidence: 99%

“…10,11 One of the seminal studies is the Lakes's theoretical analysis of a conceptual composite with extreme damping and a negative Poisson's ratio (NPR). 10 In his study, a concept of a composite system with perfect inclusions 10 is…”

Section: Introductionmentioning

confidence: 99%

Tailoring structure of inclusion with strain-induced closure to reduce Poisson's ratio of composite materials

Hou

Silberschmidt

2014

Journal of Applied Physics

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Tailoring structure of inclusion with strain-induced closure to reduce Poisson's ratio of composite materials A novel 3D continuum shell structure is introduced as inclusion for composite materials with special mechanical properties in this paper. Its geometry is based on a hollow re-entrant tetrahedron. In a composite, such an inclusion can demonstrate a closure effect induced by external compression. Its specific deformation mechanism results in a special character of deformation and affects effective (global) mechanical properties of the composite. A finite-element method is used to explore quantitatively and qualitatively the deformation mechanism of the suggested inclusion and its effect on the overall mechanical performance of the composite. In this study, geometrical features of the inclusion are used as parameters. The obtained results demonstrate that this kind of inclusion could reduce the composite's Poisson's ratio; moreover, its magnitude is adjustable by changing geometrical parameters of the inclusion. Besides, an overall hardening effect is achieved for the composite, with the magnitude of global stiffness also significantly affected by geometrical features of the inclusion. Thus, the developed inclusion actually provides a potential to develop new composites with a tunable Poisson's ratio and enhanced mechanical properties .V

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“…Partial constraint is also of interest in the context of experimental study of materials in the vicinity of phase transformations. Negative bulk modulus [18] is possible in a pre-strained lattice and in several crystalline materials. Analysis of an Ising model [19] of a lattice predicts K < 0 near the critical temperature.…”

Section: Introductionmentioning

confidence: 99%

“…Softening [20] of the bulk modulus (analogous to softening of the shear modulus in ferroelastics) has been observed in YbInCu 4 crystals at a temperature of 67 K. Composites with spherical inclusions of negative bulk moduli exhibit anomalies in the composite bulk modulus and Young's modulus (and in the corresponding mechanical damping). A partially constrained bar with negative bulk modulus is stable with respect to elementary deformation modes [18]. However, there are an infinite number of modes in a continuum.…”

Section: Introductionmentioning

confidence: 99%

Stability of elastic material with negative stiffness and negative Poisson's ratio

Shang

Lakes

2007

Physica Status Solidi (b)

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PACS 46. 05.+b, 62.20.Dc Stability of cuboids and cylinders of an isotropic elastic material with negative stiffness under partial constraint is analyzed using an integral method and Rayleigh quotient. It is not necessary that the material exhibit a positive definite strain energy to be stable. The elastic object under partial constraint may have a negative bulk modulus K and yet be stable. A cylinder of arbitrary cross section with the lateral surface constrained and top and bottom planar surfaces is stable provided the shear modulus G > 0 and -G/3 < K < 0 or K > 0. This corresponds to an extended range of negative Poisson's ratio, -∞ < ν < -1. A cuboid is stable provided each of its surfaces is an aggregate of regions obeying fully or partially constrained boundary conditions.

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Composites with Inclusions of Negative Bulk Modulus: Extreme Damping and Negative Poisson’s Ratio

Cited by 99 publications

References 35 publications

Finite-Element Modelling of the Response of the Gerbil Middle Ear to Sound

Finite-Element Modelling of the Response of the Gerbil Middle Ear to Sound

Tailoring structure of inclusion with strain-induced closure to reduce Poisson's ratio of composite materials

Stability of elastic material with negative stiffness and negative Poisson's ratio

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