Mechanical Properties of Auxetic Cellular Material Consisting of Re-Entrant Hexagonal Honeycombs (original) (raw)
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In-plane elasticity of a novel auxetic honeycomb design
Composites Part B: Engineering, 2017
This work presents a novel negative Poisson's ratio honeycomb design composed by two parts (a re-entrant hexagonal component and a thin plate part) that provide separate contributions to the in-plane and out-of-plane mechanical properties. The re-entrant hexagons provide the in-plane negative Poisson's ratio, the in-plane compliance and the out-of-plane compressive strength, while the thin plate part connecting the re-entrant hexagonal section bears the large out-of-plane flexibility. This paper focuses on the in-plane mechanical properties of the auxetic cellular structure. Theoretical models related to the in-plane uniaxial tensile modulus, the shear modulus, and the Poisson's ratios have been built and validated using the finite element techniques. The in-plane behavior of the honeycomb has also been investigated against the geometrical parameters of the unit cell using a parametrical analysis. The theoretical and numerical models illustrate good agreement and show the potential of its application in morphing structures. We also provide a benchmark of the auxetic configuration proposed in this work against negative Poisson's ratio topologies from open literature.
Cellular Polymers, 2011
Cellular solids, in particular hexagonal honeycombs have been the subject of numerous studies in the last decades in view of their extensive use in many applications. In particular, there have been various studies aimed at expressing the mechanical properties of honeycombs in terms of the geometrical parameters used to describe the structure of such honeycombs. Despite improvements over the first established model, finite element simulations performed in this work on honeycombs having ribs with a realistic thickness-to-length ratio suggest that the mechanical properties for such systems differ from those predicted by current models, sometimes to a very significant extent. In view of this, we analyse in detail the deformed structures in an attempt to gain insight into how and the extent to which the shape of the ligaments, in particular its thickness and mode of connection affects deformation in conventional and re-entrant hexagonal honeycombs. Based on these observations, we propose...
Models for Elastic Deformation of Auxetic Honeycomb with Triangular Cells
2015
Honeycomb, Auxetic, elastic, Properties, Model Studies devoted to honeycombs are aimed at improvement of their mechanical properties. One of the methods is a core structure modification by adding auxetic features. Therefore, for modelling, it is relevant and necessary to describe the deformation mechanism and honeycomb elastic constants. In the case of hexagonal cellular structures, this field is well recognized. On the other hand, there is little research dedicated to the analytical description of a deformation form in the context of material properties of non-hexagonal auxetic honeycombs. The aim of the study was to develop a theoretical model for predicting triangular auxetic core elastic constants based on cell deformation by pure flexure. Axial displacements of cell nodes were established as well as expressions for moduli of elasticity, shear moduli and Poisson's ratios. Derived dependencies showed how the material properties and the applied load direction affected the defo...
Effective in-plane elastic properties of auxetic honeycombs with spatial irregularity
An analytical framework has been developed for predicting the equivalent in-plane elastic moduli (longitudinal and transverse Young’s modulus, shear modulus, Poisson’s ratios) of irregular auxetic honeycombs with spatially random variations in cell angles. Employing a bottom up multi-scale based approach, computationally efficient closed-form expressions have been derived in this article. This study also includes development of a highly generalized finite element code capable of accepting number of cells in two perpendicular directions, random structural geometry and material properties of irregular auxetic honeycomb and thereby obtaining five in-plane elastic moduli of the structure. The elastic moduli obtained for different degree of randomness following the analytical formulae have been compared with the results of direct finite element simulations and they are found to be in good agreement corroborating the validity and accuracy of the proposed approach. The transverse Young’s modulus, shear modulus and Poisson’s ratio for loading in transverse direction (effecting the auxetic property) have been found to be highly influenced by the structural irregularity in auxetic honeycombs.
Transverse elastic shear of auxetic multi re-entrant honeycombs
Composite Structures, 2009
The paper describes the transverse shear properties of a novel centresymmetric honeycomb structure evaluated using analytical and finite element models. The cellular structure features a representative volume element (RVE) geometry allowing in-plane auxetic (negative Poisson’s ratio) deformations, and multiple topologies to design the honeycomb for multifunctional applications. The out-of-plane properties are calculated using a theoretical approach based on Voigt and Reuss bounds. The analytical models are validated using a full scale Finite Element technique to simulate transverse shear tests, a quarter FE of the RVE with periodic shear conditions and an FE homogenisation method for periodic structures. The comparison between the analytical and numerical models shows good convergence between the different set of results, and highlights the specific deformation mechanism of the multi re-entrant honeycomb cell.
On the evaluation of mechanical properties of honeycombs by using finite element analyses
INCAS BULLETIN, 2015
This paper presents some general two-and three-dimensional finite element models to study the equivalent orthotropic mechanical properties of honeycombs. The models are developed on a representative volume element with appropriate periodic boundary conditions for six load cases for three-dimensional models to obtain the in-plane and out-of-plane elastic properties of hexagonal honeycombs. The developed models use beam, solid 2D and 3D, and also shell type finite elements. The proposed models are validated using analytical relationships from literature. For this reason some aspects regarding their proper use, depending on the purpose of the analysis, are presented. It is shown that similar models can be used for different periodic cell structures as chiral and anti-chiral honeycomb structures. The developed finite element models can also be used conveniently for parametric and sensitivity analyses because the total number of degrees of freedom is relatively small compared to a complete model.
In-plane elasticity of a multi re-entrant auxetic honeycomb
Composite Structures
Honeycomb structures are essentially constituted of a repetition of regularly-arranged and loaded sub-structures. The present study carries out a parametrically investigation of the behavior of a multi re-entrant honeycomb structure with variable stiffness and Poisson's ratio effects. A refined analytical model is specifically developed and compared to full-scale numerical simulations. The analytical model developed is based on energy theorems and takes into full consideration bending, shearing and membrane effects. The influence of the cell walls thickness on the elastic homogenized constants is investigated. The results obtained show a good agreement between the refined analytical approach developed and the numerical computations carried out.
Nonlinear Elastic Constitutive Relations of Auxetic Honeycombs
Volume 11: Mechanics of Solids, Structures and Fluids, 2009
When designing a flexible structure consisting of cellular materials, it is important to find the maximum effective strain of the cellular material resulting from the deformed cellular geometry and not leading to local cell wall failure. In this paper, a finite in-plane shear deformation of auxtic honeycombs having effective negative Poisson's ratio is investigated over the base material's elastic range. An analytical model of the inplane plastic failure of the cell walls is refined with finite element (FE) micromechanical analysis using periodic boundary conditions. A nonlinear constitutive relation of honeycombs is obtained from the FE micromechanics simulation and is used to define the coefficients of a hyperelastic strain energy function. Auxetic honeycombs show high shear flexibility without a severe geometric nonlinearity when compared to their regular counterparts.
Numerical and experimental uniaxial loading on in-plane auxetic honeycombs
Journal of Strain Analysis for Engineering Design, 2000
Auxetic honeycombs show in-plane negative Poisson's ratio properties; they expand in all directions when pulled in only one, and contract when compressed. This characteristic is due to the reentrant shape of the honeycomb unit cell. The cell convoluteness gives a geometric stiffening effect that affects the linear elastic properties of the whole cellular solid. In this paper finite element simulations are carried out to calculate the in-plane Poisson's ratio and Young's moduli of re-entrant cell honeycombs for different geometric layout combinations (side cell aspect ratio, relative thickness and internal cell angle) subjected to uniaxial loading. The results show a high sensitivity of the mechanical properties for particular ranges of the geometric cell parameters. An image data detection technique is used to extract displacements and strains from an aramid paper re-entrant honeycomb sample in a tensile test. The comparison between numerical and experimental results shows good agreement.