Grandgeorge Paul, Baek Changyeob, Singh Harmeet, Johanns Paul, Sano Tomohiko G, Flynn Alastair, Maddocks John H, Reis Pedro M
Flexible Structures Laboratory, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland.
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139.
Proc Natl Acad Sci U S A. 2021 Apr 13;118(15). doi: 10.1073/pnas.2021684118.
Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear deformations, and friction. Here, we perform an in-depth study of a simple, yet canonical, problem that captures the essence of contact between filaments. In the orthogonal clasp, two filaments are brought into contact, with each centerline lying in one of a pair of orthogonal planes. Our data from X-ray tomography (μCT) and mechanical testing experiments are in excellent agreement with finite element method (FEM) simulations. Despite the apparent simplicity of the physical system, the data exhibit strikingly unintuitive behavior, even when the contact is frictionless. Specifically, we observe a curvilinear diamond-shaped ridge in the contact-pressure field between the two filaments, sometimes with an inner gap. When a relative displacement is imposed between the filaments, friction is activated, and a highly asymmetric pressure field develops. These findings contrast to the classic capstan analysis of a single filament wrapped around a rigid body. Both the μCT and FEM data indicate that the cross-sections of the filaments can deform significantly. Nonetheless, an idealized geometrical theory assuming undeformable tube cross-sections and neglecting elasticity rationalizes our observations qualitatively and highlights the central role of the small, but nonzero, tube radius of the filaments. We believe that our orthogonal clasp analysis provides a building block for future modeling efforts in frictional contact mechanics of more complex filamentary structures.
柔性细丝网络通常包含紧密接触的区域。由于拓扑结构、几何形状、大的非线性变形和摩擦之间存在复杂的耦合关系，对这些系统的平衡构型进行预测性理解具有挑战性。在此，我们对一个简单但具有代表性的问题进行了深入研究，该问题抓住了细丝间接触的本质。在正交扣合中，两根细丝相互接触，每根细丝的中心线位于一对正交平面中的一个平面内。我们通过X射线断层扫描（μCT）和力学测试实验获得的数据与有限元方法（FEM）模拟结果高度吻合。尽管该物理系统表面看似简单，但即使在无摩擦接触的情况下，数据也呈现出惊人的非直观行为。具体而言，我们在两根细丝之间的接触压力场中观察到一个曲线形的菱形脊，有时还会有一个内部间隙。当在细丝之间施加相对位移时，摩擦力被激活，会形成一个高度不对称的压力场。这些发现与经典的单根细丝缠绕刚体的绞盘分析结果形成对比。μCT和FEM数据均表明细丝的横截面会发生显著变形。尽管如此，一个理想化的几何理论，即假设管横截面不可变形并忽略弹性，在定性上解释了我们的观察结果，并突出了细丝小但非零的管半径的核心作用。我们相信，我们的正交扣合分析为未来更复杂丝状结构的摩擦接触力学建模工作提供了一个基础。
