Determination of the average characteristics of elastic frameworks

Kolpakov, A. G.

doi:10.1016/0021-8928(85)90011-5

Cited by 159 publications

(75 citation statements)

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“…Consider a two-dimensional triangular lattice system which has a positive Poisson's ratio of 0.25 (for equilateral triangles) [17]. If the stiffness of selected rib elements in the lattice is allowed to relax to zero, the remaining ligaments form (at long times) a re-entrant lattice [18,19] with a negative Poisson's ratio. A generalization of this notion is shown in Figure 2.…”

Section: Monotonicitymentioning

confidence: 99%

On Poisson’s Ratio in Linearly Viscoelastic Solids

2006

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Poisson's ratio in viscoelastic solids is in general a time dependent (in the time domain) or a complex frequency dependent quantity (in the frequency domain). We show that the viscoelastic Poisson's ratio has a different time dependence depending on the test modality chosen; interrelations are developed between Poisson's ratios in creep and relaxation. The difference, for a moderate degree of viscoelasticity, is minor. Correspondence principles are derived for the Poisson's ratio in transient and dynamic contexts. The viscoelastic Poisson's ratio need not increase with time, and it need not be monotonic with time. Examples are given of material microstructures which give rise to designed time dependent Poisson's ratios.

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Section: Monotonicitymentioning

confidence: 99%

On Poisson’s Ratio in Linearly Viscoelastic Solids

2006

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“…10(a)]. These rings have an inverted characteristic similar to re-entrant honeycombs, the typical model which induces a negative Poisson's ratio [41][42][43].…”

Section: Anisotropy Of Poisson's Ratiomentioning

confidence: 99%

Molecular dynamics study of the high‐temperature elasticity of SiO₂ polymorphs: Structural phase transition and elastic anomaly

Kimizuka

Kaburaki²

2005

Physica Status Solidi (b)

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The elastic properties of cristobalite and quartz, the typical polymorphs of SiO 2 , are studied with particular emphasis on the structural phase transition and the high-temperature phase. Using the equilibrium molecular dynamics (MD) method with a stress-fluctuation formula, we have successfully evaluated the adiabatic elastic constants ( ij C ) of both cristobalite and quartz in a wide temperature range, including the a -b phase-transition region. In the results for cristobalite, the anomalous property of a negative Poisson's ratio appears over the entire temperature range of 300 -1800 K, where the bulk modulus is extremely low compared with the shear modulus. However, the mechanisms differ between the a -and bphases, according to the structural data obtained from the MD simulations. On the other hand, quartz exhibits a negative Poisson's ratio in the narrow temperature region between ca. 750 and 825 K before the phase transition occurs. After the transition to the b -phase, the bulk modulus is shown to increase sharply, and a positive value of Poisson's ratio is recovered. For cristobalite as well as quartz, we have confirmed that the recovery of bulk ij C 's in the b -phase can be attributed to internal relaxations, which arise from the cooperative motions of corner-linked SiO 4 tetrahedra.

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“…Almost all these models are based on a simple mechanism that is treated as a unit cell leading to a global stiffening effect. Conceptually, the auxetic structure has been known since 1944 [27], but the first artificial experimental samples concerning a re-entrant structure, first proposed by Almgren [35] and Kolpakov [36], were presented in 1987 by Lakes [4]. Since then, different models have been proposed and analysed [37][38][39][40][41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Auxetic two-dimensional lattices with Poisson's ratio arbitrarily close to −1

Cabras

Brun

2014

Proc. R. Soc. A.

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In this paper, we propose a class of lattice structures with macroscopic Poisson's ratio arbitrarily close to the stability limit −1. We tested experimentally the effective Poisson's ratio of the microstructured medium; the uniaxial test was performed on a thermoplastic lattice produced with a threedimensional printing technology. A theoretical analysis of the effective properties was performed, and the expression of the macroscopic constitutive properties is given in full analytical form as a function of the constitutive properties of the elements of the lattice and on the geometry of the microstructure. The analysis was performed on three microgeometries leading to an isotropic behaviour for the cases of threeand sixfold symmetries and to a cubic behaviour for the case of fourfold symmetry.

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Determination of the average characteristics of elastic frameworks

Cited by 159 publications

References 1 publication

On Poisson’s Ratio in Linearly Viscoelastic Solids

On Poisson’s Ratio in Linearly Viscoelastic Solids

Molecular dynamics study of the high‐temperature elasticity of SiO₂ polymorphs: Structural phase transition and elastic anomaly

Auxetic two-dimensional lattices with Poisson's ratio arbitrarily close to −1

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Determination of the average characteristics of elastic frameworks

Cited by 159 publications

References 1 publication

On Poisson’s Ratio in Linearly Viscoelastic Solids

On Poisson’s Ratio in Linearly Viscoelastic Solids

Molecular dynamics study of the high‐temperature elasticity of SiO2 polymorphs: Structural phase transition and elastic anomaly

Auxetic two-dimensional lattices with Poisson's ratio arbitrarily close to −1

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About

Molecular dynamics study of the high‐temperature elasticity of SiO₂ polymorphs: Structural phase transition and elastic anomaly