Numerical Modelling of Compressive Characteristics of Auxetic Structures

Abstract

The paper is focused on numerical analysis of mechanical behaviour of auxetic structures with re-entrant tetrakaidecahedral unit cell subjected to uni-axial quasi-static compression. The mechanical behaviour was evaluated inversely with respect to selected geometrical parameters of the unit cell and two different loading modes. Finite element method was used for the numerical analysis of the problem. A set of fully parametric tools has been developed, which enabled automated execution and evaluation of virtual experiments. From results of the simulations, Young’s modulus, the characteristics of the Poisson’s ratio function, and the deformation energy density were estimated. The relation between these characteristics and geometry of the unit cell, particularly the re-entrant angle and the relative density, was evaluated. Results of the numerical simulations for the unit cell and representative volume element of its three-dimensional periodic assembly are presented.

Compressive Behaviour of Additively Manufactured Periodical Re-Entrant Tetrakaidecahedral Lattices at Low and High Strain-Rates

“…To achieve the auxetic design of the cell, the re-entrant angle as defined by Choi and Lakes [28] may vary in the range 45-90 • . Based on a prior numerical analysis [29] two versions of the unit-cell geometry, both with a re-entrant angle of 60 • , were considered in this study. The "beam" version is based on the original open-cell design and consists only of struts, while the "facet" version is designed as an assumed stiffer modification of the original cell consisting of both 1D (struts) and 2D (facets) elements.…”

“…However, this property was not evaluated in this study due to the geometry of the investigated specimens. Firstly, due to the restrictions resulting from the geometry of the dynamic experimental setup and the limited precision of the manufacturing method, the number of unit cells did not fulfil the requirements on the representative volume element (RVE) of the structure [29]. Thus, the deformation localisation exerted a strong effect on the overall response of the specimens.…”

“…The potential of such a unit-cell and lattice in deformation energy mitigation is thus unclear; such potential is also unclear when AM is used for its production instead of thermo-mechanical modification of a non-auxetic foam as considered in the original paper of Choi and Lakes. In our previous study, we performed a finite element investigation into the anticipated auxetic character of such a structure subjected to uniaxial quasi-static compression [29]. Based on our previous findings, we have exploited the advantages of a high-resolution metal PBF AM method to produce four different variants of periodic lattices based on the re-entrant tetrakaidecahedral unit-cell represented either by a beam or a facet analogy.…”

Experimental and Numerical Study on Withdrawal Strength of Different Types of Auxetic Dowels for Furniture Joints

“…The mechanical behavior was evaluated inversely with respect to selected geometrical parameters of the unit cell and two different loading modes. Finite element method was used for the numerical analysis of the problem, and from results of simulations, Young’s modulus, the characteristics of Poisson’s ratio function, and deformation energy density were estimated [ 22 ]. Patiballa and Krishnan [ 23 ] presented a new mechanics-based framework for the qualitative analysis and conceptual design of mechanical metamaterials, and specifically materials exhibiting auxetic behavior.…”