Computational Study of Non-Porous Auxetic Plates with Diamond Shape Inclusions

Abstract

Creating non-porous structures that offer auxetic behavior can have a variety of industrial applications, especially when the porosity impairs the functionality of the auxetic structures. This study presents the design and finite element analysis of architected bi-material auxetic plates consisting of repeating unit cells that comprise rigid rotary units and soft inclusions. The change in the design parameters of unit cells produces a variety of mechanical properties, such as different levels of Poisson’s ratio and stiffness for the architected plates that can result in specific static or dynamic responses. The natural frequencies and deflection under uniform lateral loading of the architected plates with clamped boundary conditions were investigated. Furthermore, the effectiveness of the homogenization technique based on the mechanical properties obtained from finite element analysis in predicting the dynamic and static response of the architected plate was also studied.

Auxetics and FEA: Modern Materials Driven by Modern Simulation Methods

“…It was shown that these inclusions still retained a negative Poisson's ratio but reduced the extent of auxeticity. This would be useful in applications of non-porous auxetic materials [105]. Similar conclusions were also drawn in an earlier FEA study by [177] which examined non-porous grooved single-material systems.…”

“…These included the double-V re-entrant system [100] and another motif [101], later referred to as the "anti-tetrachiral" motif [102][103][104] (Figure 1c). Nowadays, much more developed commercially available software such as ANSYS (Ansys Inc., Houston, TX, USA), MSC Marc (Hexagon AB, Newport Beach, CA, USA) and ABAQUS (Dassault Systèmes Simulia Corp., Johnston, RI, USA) combined with high computational power are essential tools when conducting research in the mechanical properties of materials and has, thus, been utilized by several research groups, as noted in Appendix A, in the study of auxetic metamaterials [63,[105][106][107][108][109][110][111][112][113]. It is also most useful that various textbooks have been written to guide researchers through the background theory and application of FEA [70,71,114].…”

Studies of Auxetic Structures Assembled from Rotating Rectangles

“…A number of publications on these metamaterials introduce modifications to their structure. These include building composite systems [18][19][20][21][22] or hierarchical systems [10,[23][24][25][26] or modifying the connections of the rotating polygons [21,27]. A distinct portion of research concerns the fabrication of rotating polygon structures by cutting out rhombuses from selected materials (perforated plate): polymer [12,28,29] and textiles [30].…”

Auxetic properties of a tangram-inspired metamaterial

“…An example of such study has been conducted by Strek et al [67] whereby each cell in a sandwich core consists of an auxetic structure such as rotating square or re-entrant honeycomb, and the effect of the fillers on the overall behavior of the sandwich panel was observed. In addition, there has been extensive studies of the more general 2D composites based on elliptic inclusions which in certain limits can be thought of as the rotating squares [68][69][70].…”