Elasto-static micropolar behavior of a chiral auxetic lattice
By A. Spadoni, Massimo Ruzzene. 2012
354 citations recorded by the source corpus.
Auxetic materials expand when stretched, and shrink when compressed. This is the result of a negative Poisson's ratio ν. Isotropic configurations with ν≈−1 have been designed and are expected to provide increased shear stiffness G. This assumes that Young's modulus and ν can be engineered independently. In this article, a micropolar-continuum 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 ν=−1. 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 lc of all known lattice topologies, as well as a negative first Lame constant without violating bounds required for thermodynamic stability. We also find that hexagonal arrangements of deformable rings have a coupling number N=1. This is the first lattice reported in the literature for which couple-stress or Mindlin theory is necessary rather than being adopted a priori.
Subfields: Mechanical Engineering, Polymers and Plastics
View Paper: https://www.semanticscholar.org/paper/3d40a1fd427cb90791db27b2fecca5c983aecba4
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In Mechanical Engineering
In Polymers and Plastics
Citations in the corpus
- Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices (2012, methodology): “A chiral material should be described by an adequate constitutive equation with handedness in order to characterize the distinct feature of such material.”
- Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: A simple energy-based approach (2016, background): “1 have been shown to possess relatively compliant behavior because of their bending dominated response, while exhibiting considerable multiaxial expansion/contraction under uniaxial loads due to auxeticity [32,33].”
- Mechanical metamaterials associated with stiffness, rigidity and compressibility: a brief review (2017, background): “Similar levels of auxeticity consist of microporous polymers [357], pattern transformation [26,226,235], nanotube metamaterials [225], and chirality [142,329].”
- Chiral three‐dimensional isotropic lattices with negative Poisson's ratio (2016, neutral): “Chiral 2D lattices [2] have been analyzed [23, 24] in the context of Cosserat elasticity.”
- Chiral three-dimensional lattices with tunable Poisson’s ratio (2016, neutral): “For example, chiral lattices [1] have been analyzed [19] [20] in the context of Cosserat elasticity.”
- Controllable thermal expansion of large magnitude in chiral negative Poisson's ratio lattices (2015, background): “Analysis shows this lattice has the largest Cosserat characteristic length scale of all known lattice topologies [12].”
- Homogenization of periodic hexa- and tetrachiral cellular solids (2014, methodology): “The constitutive equations (6) show the coupling between the extensional strains 11Γ and 22Γ and the asymmetric strains 12Γ and 21Γ through the elastic constant A, not considered in the formulation of Spadoni and Ruzzene, 2012.”
- Auxetic mechanical metamaterials: from soft to stiff (2023, background): “Spadoni and Ruzzene [121] employed a micropolar-continuum model to analyze the in-plane elastic behavior of the hexachiral honeycomb and obtained an isotropic Poisson’s ratio of −1 when the circular node of the hexachiral structure is stiff.”
- Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing (2015, background): “Furthermore, when boundary effects could be minimized, analytical modeling also possesses an advantage over the homogenization methods due to the closed-form expressions (Gonella and Ruzzene, 2008; Spadoni and Ruzzene, 2012).”