Continuum-based stability of anisotropic and auxetic beams

Heyliger, Paul R.

doi:10.1016/j.mechrescom.2015.06.016

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…For a comprehensive survey on auxetic materials and structures, the reader is referred to a recent review and monograph. [27,28] While the early and subsequent years of auxetic research has been performed on micromechanical modeling to understand the structure-property-processing relationships that give rise to auxetic behavior in bulk solids, there has been an increasing trend toward effort to comprehend the effect of auxeticity on membranes, [29][30][31] rods, [32][33][34] beams, [35][36][37] shells, [38][39][40] and plates. [41][42][43][44] In the case of plates, the effect of material auxeticity has been investigated on problems of the following mechanical nature: a) static, [45][46][47][48] b) dynamic, [49][50][51][52][53][54] c) thermoelasticity and/or thermal stresses, [55][56][57][58][59] d) instability, [59][60][61][62] e) first-order and higher-order shear deformation, [62][63][64][65][66][67] as well as f) plates of unconventional shapes.…”

Section: Introductionmentioning

confidence: 99%

An Accurate Design Equation for the Maximum Deflection in a Class of Auxetic Sectorial Plates

Lim

2017

Physica Status Solidi (b)

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Auxetic materials are solids that exhibit negative Poisson's ratio. The effect of material auxeticity (i.e., negativity of Poisson's ratio) is investigated herein on the maximum deflection of sectorial plates with Simply‐Supported straight edges and Free curve edge (SSF). To aid the designer, an accurate and conveniently executable semi‐empirical model has been developed herein, which is valid for the entire range of Poisson's ratio of isotropic solids and for the plate's sectorial angle from 30 to 90 degrees. Results from exact solution reveal that the maximum deflection reduces sharply with the reduction of Poisson's ratio from positive to mildly negative, but deflection reduction is marginal when the sectorial plate's Poisson's ratio changes from moderately negative to highly negative value. It is therefore suggested that (a) the use of auxetic materials is useful to limit the extent of SSF sectorial plate deflection, and that (b) the use of the developed semi‐empirical model herein as a design equation gives greatly simplified but highly accurate maximum deflection prediction for SSF plates made from both conventional (positive Poisson's ratio) and auxetic (negative Poisson's ratio) materials.

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Section: Introductionmentioning

confidence: 99%

An Accurate Design Equation for the Maximum Deflection in a Class of Auxetic Sectorial Plates

Lim

2017

Physica Status Solidi (b)

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“…[ 64 ] Due to the negative value of Poisson's ratio, auxetic materials exhibit unique properties in comparison with nonauxetics such as enhanced shear modulus, indentation resistance, and fracture toughness, which were presented by Liu and Hu. [ 65 ] Where structural elements are concerned, investigations have been made on auxetic materials in the form of rods, [ 66–73 ] shells, [ 74–76 ] and especially on plates. [ 77–107 ] However, understanding on the effect of auxeticity on membranes is very few.…”

Section: Introductionmentioning

confidence: 99%

Maximum Stresses in Rectangular Auxetic Membranes

Lim

2020

Physica Status Solidi (b)

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Auxetic materials exhibit a negative Poisson's ratio. Herein, the performance of rectangular auxetic membranes, under uniform load, is evaluated in terms of the maximum stress encountered. To facilitate convenient calculation, empirical modeling is conducted on the exact solution to reproduce displacement coefficients that are sufficiently accurate. A dimensionless maximum stress is then introduced to allow the effect from the membrane's Poisson's ratio and aspect ratio to be directly observed. Results reveal that 1) the dimensionless maximum stress reduces monotonically and nonmonotonically for conventional and auxetic membranes, respectively, 2) for the same Poisson's ratio magnitude the stresses in auxetic membranes are lower than those from conventional ones, 3) the optimal Poisson's ratio, on the basis of dimensionless maximum stress minimization, falls within the negative range, and 4) the dimensionless maximum stress minimization is especially effective for square membranes as well as very long and narrow membranes. It is therefore recommended that material auxeticity be taken into account-alongside geometrical and other material properties-in designing membranes and highly compliant very thin plates.

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“…In a few studies, the mechanics of auxetic beams were investigated. For instance, the buckling behavior of anisotropic-auxetic beams were investigated in (Heyliger, 2015). Hadjigeorgiou and Stavroulakis (2004) demonstrated the applicability of auxetic cantilever beams for smart structures.…”

Section: Introductionmentioning

confidence: 99%

Poisson's ratio effects on the mechanics of auxetic nanobeams

Faroughi

Shaat

2018

European Journal of Mechanics - A/Solids

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Poisson's ratio is an important mechanical property that reveals the deformation patterns of materials. A positive Poisson's ratio is a feature of the majority of materials. Some materials, however, display "auxetic" behaviors (i.e. possess negative Poisson's ratios). Indeed, auxetic and non-auxetic materials display different deformation mechanisms. Revealing these differences and their effects on the mechanics of these materials is of a significant importance.In this study, effects of Poisson's ratio on the mechanics of auxetic and non-auxetic nanobeams are revealed. A parametric study is provided on effects of Poisson's ratio on the static bending and free vibration behaviors of auxetic nanobeams. The general nonlocal theory is employed to model the nonlocal effects. Unlike Eringen's nonlocal theory, the general nonlocal theory uses different attenuation functions for the longitudinal and lateral strains. This theory can reveal the Poisson's ratio-nonlocal coupling effects on the mechanics of nanomaterials. The obtained results showed that Poisson's ratio is an essential parameter for determining mechanical behaviors of nanobeams. It is revealed that auxetic and non-auxetic nanobeams may reflect softening or hardening behaviors depending on the ratio of the nonlocal fields of the beam's longitudinal and lateral strains.

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Continuum-based stability of anisotropic and auxetic beams

Cited by 4 publications

References 15 publications

An Accurate Design Equation for the Maximum Deflection in a Class of Auxetic Sectorial Plates

An Accurate Design Equation for the Maximum Deflection in a Class of Auxetic Sectorial Plates

Maximum Stresses in Rectangular Auxetic Membranes

Poisson's ratio effects on the mechanics of auxetic nanobeams

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