Edge Effects of a Hexagonal Honeycomb on the Poisson's Ratio and Young's Modulus,Physica Status Solidi (B) - Basic Solid State Physics

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Edge Effects of a Hexagonal Honeycomb on the Poisson's Ratio and Young's Modulus
Physica Status Solidi (B) - Basic Solid State Physics ( IF 1.5 ) Pub Date : 2020-06-26 , DOI: 10.1002/pssb.201900511
Pierre-Sandre Farrugia ₁ , Ruben Gatt ₁ , Sebastiaan De Vrieze _{1,

2} , Christos Mellos ₁ , Joseph N. Grima ₁

Affiliation

The flexing of the ligaments at the edge of a finite hexagonal honeycomb array is studied using analytical and numerical methods. It is shown that when compressed axially, the ligaments on the border of a hexagonal honeycomb array bend outwardly in contrast to the interior ligaments that bend to a negligible extent, if at all. This boundary effect reduces the overall auxeticity of re‐entrant hexagonal honeycombs. Analytical expressions that account for the edge effects on the Poisson's ratio and Young's modulus are obtained using Castigliano's second theorem. These are then tested against numerical simulations showing good agreement at least for the values of the parameters used. Additional investigations indicate that the use of a larger ligament thickness for the ligaments residing on the border of the system mitigates this edge effect on the Poisson's ratio.

中文翻译：

六角蜂窝对泊松比和杨氏模量的边缘效应

使用解析和数值方法研究了有限六角形蜂窝阵列边缘处的韧带弯曲。结果表明，当轴向压缩时，六角形蜂窝阵列边界上的韧带向外弯曲，而内部韧带则弯曲到可以忽略的程度。这种边界效应降低了凹角六角形蜂窝的整体膨胀性。使用Castigliano的第二定理获得了说明了泊松比和杨氏模量的边缘效应的解析表达式。然后针对数值模拟对它们进行测试，数值模拟显示出至少对于所用参数的值具有良好的一致性。

更新日期：2020-06-26

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