Computer simulations of auxetic foams in two dimensions
Computer simulations of auxetic foams in two dimensions
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DOI：
10.1088/0964-1726/22/8/084009
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发表时间：
2013-07
影响因子：
4.1
通讯作者：
A. Poźniak;J. Smardzewski;K. Wojciechowski
中科院分区：
文献类型：
--
作者：
A. Poźniak;J. Smardzewski;K. Wojciechowski
通过计算机模拟研究了二维拉胀（即负泊松比）泡沫的两个简单模型。在第一个模型中，进一步称为 Y 模型，形成泡沫单元的肋在对应于无序蜂窝晶格的位置的点处连接。在第二个模型中，创造了 Δ 模型，肋骨的连接不是点状的，而是空间的。为简单起见，它们由以蜂窝格点为中心的三角形表示。每个模型考虑三种接头：软接头、普通接头和硬接头，分别对应杨氏模量比筋小十倍、等于和大十倍的材料。初始晶格被均匀压缩，其线性尺寸减少了约 15%。然后将所得结构用作没有内应力的参考结构。这些参考结构的泊松比是通过在 x 或 y 方向上拉伸它们来确定的。将有限网格和有限样本获得的结果分别外推到无限细网格和热力学极限。外推表明，肋骨上只有 13 个节点的网格和小至包含 16 × 16 个单元的样本在实验的统计精度（即百分之几）内近似于无限尺寸和无限网格分辨率的系统的泊松比。模拟表明，通过应用更硬的接头，可以达到更低的泊松比，即具有更多拉胀性能的泡沫。从所执行的模拟中还可以看出，Δ 模型的泊松比低于 Y 模型。最后，将使用细网格对样本进行的模拟与用 Timoshenko 梁近似肋的模拟进行比较。考虑到后一个模型的简化，一致性出奇地好。
Two simple models of two-dimensional auxetic (i.e. negative Poisson’s ratio) foams are studied by computer simulations. In the first one, further referred to as a Y-model, the ribs forming the cells of the foam are connected at points corresponding to sites of a disordered honeycomb lattice. In the second one, coined a Δ-model, the connections of the ribs are not point-like but spatial. For simplicity, they are represented by triangles centered at the honeycomb lattice points. Three kinds of joints are considered for each model, soft, normal and hard, respectively corresponding to materials with Young’s modulus ten times smaller than, equal to and ten times larger than that of the ribs. The initial lattices are uniformly compressed, which decreases their linear dimensions by about 15%. The resulting structures are then used as reference structures with no internal stress. The Poisson’s ratios of these reference structures are determined by stretching them, in either the x or the y direction. The results obtained for finite meshes and finite samples are extrapolated to infinitely fine mesh and to the thermodynamic limit, respectively. The extrapolations indicate that meshes with as few as 13 nodes across a rib and samples as small as containing 16 × 16 cells approximate the Poisson’s ratios of systems of infinite size and infinite mesh resolution within the statistical accuracy of the experiments, i.e. a few per cent. The simulations show that by applying harder joints one can reach lower Poisson’s ratios, i.e. foams with more auxetic properties. It also follows from the simulations performed that the Δ-model gives lower Poisson’s ratios than the Y-model. Finally, the simulations using fine meshes for the samples are compared with the ones in which the ribs are approximated by Timoshenko beams. Taking into account simplifications in the latter model, the agreement is surprisingly good.