Negative Poisson's ratios in composites with star-shaped inclusions: a numerical homogenization approach

Theocaris, P. S.; Stavroulakis, Georgios Ε.; Panagiotopoulos, P. D.

doi:10.1007/s004190050117

Cited by 218 publications

(102 citation statements)

References 19 publications

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“…Interest in these unique materials has since grown significantly and a number of auxetic configurations have been proposed, both chiral (Prall and Lakes, 1997;Grima et al, 2008) or not invariant with respect to reflections, and non-chiral (Gaspar et al, 2005;Lakes, 1991;Smith et al, 2000;Theocaris et al, 1997). Envisioned applications include indentation-resistant materials (Evans and Alderson, 2000;Lakes, 1987;Lakes and Elms, 1993;Smith et al, 1999), doubly curved panels with synclastic curvature (Evans, 1990;Evans and Alderson, 2000;Lakes, 1987), and miniaturized sandwich cores (Doyoyo and Hu, 2006).…”

Section: Introductionmentioning

confidence: 99%

“…Classical elasticity theory has been previously and successfully used to describe an equivalent continuum with auxetic properties (Gaspar et al, 2005;Grima et al, 2008;Lakes, 1991;Prall and Lakes, 1997;Smith et al, 2000;Theocaris et al, 1997). Negative Poisson's and increased shear resistance in fact do not describe the behavior of internal members but rather than of a bulk material made of may cells.…”

Section: Introductionmentioning

confidence: 99%

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Elasto-static micropolar behavior of a chiral auxetic lattice

Spadoni

Ruzzene

2012

Journal of the Mechanics and Physics of Solids

293

158

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a b s t r a c tAuxetic materials expand when stretched, and shrink when compressed. This is the result of a negative Poisson's ratio n. Isotropic configurations with n % À1 have been designed and are expected to provide increased shear stiffness G. This assumes that Young's modulus and n can be engineered independently. In this article, a micropolarcontinuum model is employed to describe the behavior of a representative auxetic structural network, the chiral lattice, in an attempt to remove the indeterminacy in its constitutive law resulting from n ¼ À1. While this indeterminacy is successfully removed, it is found that the shear modulus is an independent parameter and, for certain configurations, it is equal to that of the triangular lattice. This is remarkable as the chiral lattice is subject to bending deformation of its internal members, and thus is more compliant than the triangular lattice which is stretch dominated. The derived micropolar model also indicates that this unique lattice has the highest characteristic length scale l c of all known lattice topologies, as well as a negative first Lamé constant without violating bounds required for thermodynamic stability. We also find that hexagonal arrangements of deformable rings have a coupling number N ¼1. This is the first lattice reported in the literature for which couple-stress or Mindlin theory is necessary rather than being adopted a priori.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Elasto-static micropolar behavior of a chiral auxetic lattice

Spadoni

Ruzzene

2012

Journal of the Mechanics and Physics of Solids

293

158

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“…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]. In the chiral structure proposed by Prall & Lakes [48], the basic unit is formed by connecting straight ligaments to central nodes and the auxetic effect is achieved through wrapping or unwrapping of the ligaments around the nodes in response to an applied force.…”

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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“…1); then, some accurate solutions are available for those special cases [23][24][25][26][27][28], which may be helpful for discussing mechanical properties of composites. Recently, some investigations have been made for disordered array [29] using such as homogenization method [30][31][32][33][34][35][36][37]. These results are useful for evaluating actual composites; however, if the shape and arrangement of inclusions are changed a little, we have to reconsider the effective properties.…”

Section: Introductionmentioning

confidence: 99%

Effective Young's Modulus of a Composite Including Two Groups of Periodically Arranged Inclusions

Noda

Nisitani

Takase

et al. 2002

Journal of the Society of Materials Science, Japan

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In this paper, the effects of shape and arrangement of inclusions on the effective Young's modulus of materials are considered by the application of the finite element method through examining a model, which has two groups of periodically arranged inclusions in a matrix. Here, two groups of inclusions A and B are considered, both having equally shaped equally arranged inclusions, which have the same elastic constants but different from the ones of the matrix. This model includes square and hexagonal arrays of inclusions as its special cases. First, the effect of shape of inclusions on the Young's modulus of composite materials is considered from the comparison between the results of rectangular and elliptical inclusions. Next, when the position of group A is fixed, the effect of location of group B is considered. Then the effective elastic Young's modulus is almost independent of the location of group B if the projected areas of groups A and B are not overlapped. In conclusion, the volume fraction of inclusion and projected area fraction of inclusions are found to be two major parameters controlling the effective Young's modulus of composites.

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Negative Poisson's ratios in composites with star-shaped inclusions: a numerical homogenization approach

Cited by 218 publications

References 19 publications

Elasto-static micropolar behavior of a chiral auxetic lattice

Elasto-static micropolar behavior of a chiral auxetic lattice

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

Effective Young's Modulus of a Composite Including Two Groups of Periodically Arranged Inclusions

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