Non-standard coupled extensional and bending bias tests for planar pantographic lattices. Part I: numerical simulations
Non-standard coupled extensional and bending bias tests for planar pantographic lattices. Part I: numerical simulations
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平面缩放网格的非标准耦合拉伸和弯曲偏置测试。
DOI：
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发表时间：
2016
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通讯作者：
N. Rizzi
中科院分区：
文献类型：
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作者：
E. Turco;K. Barcz;M. Pawlikowski;N. Rizzi
在dell'Isola et al.（Zeitschrift für Angewandte Math und Physik 66（6）：3473-3498，2015，Proc R Soc Lond A Math Phys Eng Sci 472（2185），2016）中，提出了缩放片的概念。目的是设计一种超材料，其显示：（i）大范围的弹性响应;（ii）在拉伸变形中的极端韧性;（iii）韧性和重量之间的方便比率。然而，这些所需的属性必须共存的非有害的机械特性，在其他类型的强加位移的存在。本文的目的是通过数值模拟证明，缩放板可以有效地抵抗弯曲和拉伸耦合变形。介绍的四参数模型显示了其多功能性，因为它能够涵盖所有考虑类型的（大）变形。我们使用的数值积分方案是基于Turco等人开发的相同概念。（Zeitschrift für Angewandte Math und Physik 67（4）：1-28，2016）：他们证明了Hencky型离散化在非线性大变形和大位移区域也非常有效。在本文的第二部分，我们将表明，所使用的模型是非常有效的描述实验证据。
In dell’Isola et al. (Zeitschrift für Angewandte Math und Physik 66(6):3473–3498, 2015, Proc R Soc Lond A Math Phys Eng Sci 472(2185), 2016), the concept of pantographic sheet is proposed. The aim is to design a metamaterial showing: (i) a large range of elastic response; (ii) an extreme toughness in extensional deformation; (iii) a convenient ratio between toughness and weight. However, these required properties must coexist with non-detrimental mechanical characteristics in the presence of other kinds of imposed displacements. The aim of this paper is to prove via numerical simulations that pantographic sheets may effectively resist to coupled bending and extensional deformations. The four-parameter model introduced shows its versatility as it is able to encompass all the considered types of (large) deformations. The numerical integration scheme which we use is based on the same concepts exploited in Turco et al. (Zeitschrift für Angewandte Math und Physik 67(4):1–28, 2016): They prove that the Hencky-type discretization is very efficient also in nonlinear large deformations and large displacements regimes. In Part II of this paper, we will show that the used models are very effective to describe experimental evidence.