Auxetic deformations and elliptic curves
Auxetic deformations and elliptic curves
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DOI：
10.1016/j.cagd.2018.02.003
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发表时间：
2018-03-01
影响因子：
1.5
通讯作者：
Streinu, Ileana
中科院分区：
文献类型：
--
作者：
Borcea, Ciprian S.;Streinu, Ileana
在材料科学和工程中，伸展行为指的是柔性结构的变形，其中在某个方向上的拉伸涉及横向加宽，而不是横向收缩。我们解决了检测柔性周期杆-节点框架的伸缩行为的问题。目前，唯一已知的算法解决方案是基于固定维半定规划这一相当繁重的机器。本文提出了一种新的、更简单的算法，它适用于一个自然的三自由度三维周期杆系框架。这一类包括大多数沸石结构，这些结构对计算材料科学的应用非常重要。我们证明了伸展变形的存在与伴随的椭圆曲线的性质有关。通过定义曲线的三次型的经典Aronhold不变量，得到了一种识别扩展能力的快速算法。相关的算法选择也被考虑在内。(C)2018爱思唯尔B.V.保留所有权利。
In materials science and engineering, auxetic behavior refers to deformations of flexible structures where stretching in some direction involves lateral widening, rather than lateral shrinking. We address the problem of detecting auxetic behavior for flexible periodic bar-and-joint frameworks. Currently, the only known algorithmic solution is based on the rather heavy machinery of fixed-dimension semi-definite programming. In this paper we present a new, simpler algorithmic approach which is applicable to a natural family of three-dimensional periodic bar-and-joint frameworks with three degrees of freedom. This class includes most zeolite structures, which are important for applications in computational materials science. We show that the existence of auxetic deformations is related to properties of an associated elliptic curve. A fast algorithm for recognizing auxetic capabilities is obtained via the classical Aronhold invariants of the cubic form defining the curve. Related algorithmic alternatives are also considered. (C) 2018 Elsevier B.V. All rights reserved.