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We propose in this paper analytical and numerical models that describe the in-plane uniaxial elastic properties (Young's moduli and Poisson's ratios) of a honeycomb structure with curved walls. We perform a parametric analysis of the mechanical performance of this honeycomb also by taking into account the different types of deformations acting inside the cell walls. The curved wall honeycomb possesses higher magnitudes of the Poisson's ratio ν12 in the auxetic configuration compared to classical center symmetric configuration with straight cell wall. The presence of the curvature also allows creating configurations with positive Poisson's ratio even for negative internal cell angles, and makes this honeycomb design attractive for mechanical tailoring. [ABSTRACT FROM AUTHOR]

Chiral systems are a class of structures, which may exhibit the anomalous property of a negative Poisson's ratio. Proposed by Wojciechowski and implemented later by Lakes, these structures have aroused interest due to their remarkable mechanical properties and numerous potential applications. In view of this, this paper investigates the on-axis mechanical properties of the general forms of the flexing anti-tetrachiral system through analytical and finite element models. The results suggest that these are highly dependent on the geometry (the ratio of ligament lengths, thicknesses, and radius of nodes) and material properties of the constituent materials. We also show that the rigidity of an anti-tetrachiral system can be changed without altering the Poisson's ratio. The anti-tetrachiral system, with the unit cell shown in red. [ABSTRACT FROM AUTHOR]

Honeycombs or foams with reentrant microstructures exhibit effective negative Poisson's ratio. Although they are light weight due to inherently empty space, their overall stiffness and damping are somewhat limited. With judiciously chosen filler material to fill the voids in star‐shaped honeycomb, it is numerically demonstrated its auxeticity may be enhanced. By combining the filler and skeleton, the hierarchical composite materials are constructed. The magnitude of the enhancement depends on inner and outer filler's modulus mismatch, as well as the types of filling. Filler's auxeticity also largely enhances overall auxeticity of the outer‐ and all‐filled honeycomb. In addition, for outer‐filled honeycomb, its effective viscoelastic modulus and damping are significantly increased, while maintaining relatively light weight, due to local stress concentration. [ABSTRACT FROM AUTHOR]

A chiral 3D lattice is designed, made by 3D printing, and studied experimentally. The lattice exhibits squeeze–twist coupling and a Poisson's ratio near zero. Squeeze–twist coupling does not occur in classical elasticity which makes no provision for chirality. By contrast, chiral effects are allowed in Cosserat elasticity. An experimental squeeze–twist coupling strain ratio on the order of unity and a Poisson's ratio near zero are in reasonable agreement with prior finite element analysis of a lattice with similar structure, for which negative Poisson's ratio is anticipated for a sufficient number of cells. [ABSTRACT FROM AUTHOR]

Microstructured plates, consisting of various conventional and re-entrant cells, are numerically constructed and analyzed for their effective elastic properties under in-plane deformation. The finite element numerical method is adopted. The calculated effective Poisson's ratios of the plates are found to be in the range between −1 and 1, in consistency with the theory of two-dimensional elasticity. Auxetic angles need to be greater than about 20° in order to obtain negative Poisson's ratio. Increasing the auxetic angles reduces the effective pure shear modulus. Elastically anisotropic characteristics of the homogenized plate are analyzed with the calculated effective Young's modulus, Poisson's ratio, and pure shear modulus. [ABSTRACT FROM AUTHOR]

Chiral three-dimensional isotropic cubic lattices with rigid cubical nodules and multiple deformable ribs are developed and analyzed via finite element analysis. The lattices exhibit geometrydependent Poisson's ratio that can be tuned to negative values. Poisson's ratio decreases from positive to negative values as the number of cells increases. Isotropy is obtained by adjustment of aspect ratio. The lattices exhibit significant size effects. Such a phenomenon cannot occur in a classical elastic continuum but it can occur in a Cosserat solid. [ABSTRACT FROM AUTHOR]

Using Finite Element computer simulations, Poisson's ratio (PR) is determined for anti-chiral structures built on rectangular lattices with disorder introduced by stochastic distributions of circular node sizes. The investigated models are parameterized by the lattice anisotropy, the rib thickness, and the radii distribution of circular nodes. Three approaches are developed. The first approach, exact in the limit of infinitely large system and infinitely dense mesh, uses only planar elements (CPS3). Two other approaches are approximate and exploit one-dimensional elements utilizing the Timoshenko beam theory. It is shown that in the case of sufficiently large anisotropy of the studied structures PR can be highly negative, reaching any negative value, including those lower than [ABSTRACT FROM AUTHOR]

An investigation of Poisson's ratios and band gap behaviors of 2D hierarchical re‐entrant lattice structures is conducted using finite element method (FEM). The structure with a hierarchy order n (n≥1) is constructed by replacing each outmost vertex of the re‐entrant octagons of a hierarchical structure of hierarchy order n−1 with a smaller self‐similar re‐entrant octagon. The dispersion relation and transmission spectrum of the proposed hierarchical structures are analyzed based on the Bloch's theorem. The effects of geometrical parameters, order of rotational symmetry and orientation angle of some types of re‐entrant polygon cores on the lattice Poisson's ratio and band gap structures are also investigated. Results show that the re‐entrant structures with first order hierarchy exhibit a wider band gap and a stronger attenuation effect compared with structures without structural hierarchy. The first order 2D hierarchical re‐entrant structure with a negative Poisson's ratio of −0.032 exhibits the widest band gap, 17.8% wider than that of the zeroth order 2D re‐entrant structure. The order of rotational symmetry and the orientation angle of the re‐entrant polygon cores of the lattice have a strong impact on the lattice Poisson's ratio and band structures. [ABSTRACT FROM AUTHOR]