Geometry: The leading parameter for the Poisson's ratio of bending-dominated cellular solids
Geometry: The leading parameter for the Poisson's ratio of bending-dominated cellular solids
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DOI：
10.1016/j.ijsolstr.2016.06.027
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发表时间：
2016-12-01
影响因子：
3.6
通讯作者：
Schroder-Turk, Gerd E.
中科院分区：
文献类型：
--
作者：
Mitschke, Holger;Schury, Fabian;Schroder-Turk, Gerd E.
控制蜂窝结构响应于施加的外力而显示的变形行为是机械超材料的有效设计的要求，特别是具有负泊松比的那些。本文揭示了几何微观结构和力学响应之间的关系的老问题，通过比较的变形性能的酒吧和关节框架与他们的实现作为一个细胞固体由线弹性材料。对于有序平面镶嵌模型，我们发现了一种根据框架模型自由度的分类：首先，在几何形状唯一规定框架模型的单一变形模式的情况下，线弹性胞状固体的机械变形和泊松比紧密地遵循唯一变形模式的那些;结果是弯曲主导的变形，有效泊松比对下面材料的泊松比的依赖性可以忽略，有效杨氏模量的值很小。第二，在刚性结构的情况下，或当几何退化防止弯曲为主的变形模式，有效泊松比是材料依赖性的和杨氏模量（E）在波浪线（CS）大。这种类型的所有分析结构都具有泊松比的正值和（E）超过波浪线（cs）的大值。第三，在框架具有多种变形模式的情况下，仅几何形状不足以确定机械变形。这些结果阐明了线弹性胞状固体的力学性质与其相应的杆-关节框架抽象之间的关系。他们还提出了一个问题，如果在本质上，拉胀行为被限制到几何形状引导类的弯曲为主的结构对应于独特的机制，具有固有的低值的杨氏模量。(C)2016爱思唯尔有限公司版权所有
Control over the deformation behaviour that a cellular structure shows in response to imposed external forces is a requirement for the effective design of mechanical metamaterials, in particular those with negative Poisson's ratio. This article sheds light on the old question of the relationship between geometric microstructure and mechanical response, by comparison of the deformation properties of bar-and-joint frameworks with those of their realisation as a cellular solid made from linear-elastic material. For ordered planar tessellation models, we find a classification in terms of the number of degrees of freedom of the framework model: first, in cases where the geometry uniquely prescribes a single deformation mode of the framework model, the mechanical deformation and Poisson's ratio of the linearly-elastic cellular solid closely follow those of the unique deformation mode; the result is a bending-dominated deformation with negligible dependence of the effective Poisson's ratio on the underlying material's Poisson's ratio and small values of the effective Young's modulus. Second, in the case of rigid structures or when geometric degeneracy prevents the bending-dominated deformation mode, the effective Poisson's ratio is material-dependent and the Young's modulus (E) over tilde (cs) large. All analysed structures of this type have positive values of the Poisson's ratio and large values of (E) over tilde (cs). Third, in the case, where the framework has multiple deformation modes, geometry alone does not suffice to determine the mechanical deformation. These results clarify the relationship between mechanical properties of a linear-elastic cellular solid and its corresponding bar-and-joint framework abstraction. They also raise the question if, in essence, auxetic behaviour is restricted to the geometry-guided class of bending-dominated structures corresponding to unique mechanisms, with inherently low values of the Young's modulus. (C) 2016 Elsevier Ltd. All rights reserved.