Finite Element Modeling of Tight Elastic Knots
Finite Element Modeling of Tight Elastic Knots
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DOI：
10.1115/1.4049023
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发表时间：
2021-02-01
影响因子：
2.6
通讯作者：
Reis, Pedro M.
中科院分区：
文献类型：
--
作者：
Baek, Changyeob;Johanns, Paul;Reis, Pedro M.
我们提出了一种方法来模拟力学的节在弹性棒使用几何非线性，全三维（3D）有限元分析。我们关注的是紧密结构中节点的力学行为，因此必须考虑到完整的3D变形。为了设置我们的打结结构的拓扑结构，我们将一系列规定的位移步骤应用于与3D实体元素网格化的初始直杆的中心线。自接触是由一个法向惩罚力和库仑摩擦相结合来实现的。作为测试用例，我们调查了右手结和8字形结。我们的模拟通过精密模型实验验证，结合杆制造和x射线断层扫描。即使将重点放在方法上，我们的结果也表明，紧弹性结的三维变形是其机械响应的核心。这些发现与之前对松散结的分析形成了对比，之前基于1D中心线的杆理论足以预测。我们的方法可以作为一个强大的框架来访问紧密结结构的复杂力学行为，这些结构不容易通过实验或现有的降阶理论获得。
We present a methodology to simulate the mechanics of knots in elastic rods using geometrically nonlinear, full three-dimensional (3D) finite element analysis. We focus on the mechanical behavior of knots in tight configurations, for which the full 3D deformation must be taken into account. To setup the topology of our knotted structures, we apply a sequence of prescribed displacement steps to the centerline of an initially straight rod that is meshed with 3D solid elements. Self-contact is enforced with a normal penalty force combined with Coulomb friction. As test cases, we investigate both overhand and figure-of-eight knots. Our simulations are validated with precision model experiments, combining rod fabrication and X-ray tomography. Even if the focus is given to the methods, our results reveal that 3D deformation of tight elastic knots is central to their mechanical response. These findings contrast to a previous analysis of loose knots, for which 1D centerline-based rod theories sufficed for a predictive understanding. Our method serves as a robust framework to access complex mechanical behavior of tightly knotted structures that are not readily available through experiments nor existing reduced-order theories.