[论文解读] On the failure of beam-like topologically interlocked structures

Ioannis Koureas, Mohit Pundir+2 more|arXiv (Cornell University)|Jul 4, 2022

Adhesion, Friction, and Surface Interactions被引用 1

一句话总结

本研究采用耦合有限元与解析方法，探究梁状拓扑互锁结构（TIS）的失效机理，重点关注摩擦、几何形状与材料性能之间的相互作用。研究发现，结构高度与摩擦系数的组合决定了失效是受滑移还是黏着控制，揭示了机械性能的普遍饱和极限，该极限由界面黏着与块体转动决定，与材料或几何设计无关。

ABSTRACT

Topologically interlocked structures are architectured by fitting together blocks that are constrained geometrically through contact and friction by their neighboring blocks. As long as the frictional strength is nowhere exceeded, the blocks stick against each other, allowing for large rotations. Once the interfacial stresses exceed the frictional strength, relative sliding between the blocks alters the structure's mechanical response. Improving the structural performance, precisely the strength and the toughness, has been one of the main focal points in the literature. However, many fundamental questions regarding the role and effect of the interface mechanisms (stick and slip) and rotation of the blocks have not been addressed yet. Here, we carry out a parametric analysis to understand the effect of Young's modulus, friction coefficient and geometry of the blocks on the dominance of the stick or slip governed mechanism. We combine analytical and computational tools to analyze the failure mechanisms and the response capacities of beam-like topologically interlocked structures. This is achieved using a finite element method coupled with a penalty-based approach for enforcing contact constraints along interfaces. We show that the combination of the structure's height and the friction coefficient controls whether the failure mechanism is slip-governed or stick-governed. Furthermore, we demonstrate that the sticking mechanism across all interfaces along with the rotation of the blocks dictates a saturation level to the mechanical performance of a given structure irrespective of geometric and material properties. This provides a theoretical upper bound for the structural response of topologically interlocked structures and establishes a theoretical benchmark of achievable performance.

研究动机与目标

• 阐明杨氏模量、摩擦系数及块体几何形状如何影响TIS失效机制是受滑移还是黏着控制。
• 量化在黏着主导与滑移主导响应下，结构承载能力、能量吸收、刚度与挠度等性能指标。
• 通过识别界面黏着与块体转动引起的机械响应饱和水平，建立TIS性能的理论上限。
• 通过分离界面力学的作用，为TIS可实现性能提供一个与材料或几何参数无关的基准。

提出的方法

• 采用罚函数接触算法的有限元法（FEM），以施加块体之间的摩擦接触约束。
• 利用桁架模型近似推导纯黏着条件下承载能力的解析表达式。
• 通过参数研究，改变杨氏模量（E）、摩擦系数（µ）与结构高度（h），评估其对失效模式主导性的影响。
• 通过Cattaneo-Mindlin接触问题的解析解验证FEM模拟结果，确保接触力预测的准确性。
• 进行网格收敛性分析与罚参数敏感性分析，以确保数值鲁棒性并最小化界面穿透。
• 基于库仑摩擦定律与桁架模型几何，推导出从黏着到滑移行为转变的理论阈值。

实验结果

研究问题

• RQ1 杨氏模量、摩擦系数与几何参数如何影响TIS中失效机制是受滑移还是黏着控制？
• RQ2 界面黏着与块体转动在限制TIS最大机械性能方面起什么作用？
• RQ3 能否建立一个与材料和几何设计无关的结构响应理论上限？
• RQ4 结构高度与摩擦系数的组合如何决定梁状TIS中的主导失效机制？
• RQ5 局部滑移事件以及黏着与滑移共存对整体刚度与承载能力的影响程度如何？

主要发现

• 梁状TIS中滑移或黏着主导失效的主导性，主要由结构高度与摩擦系数的组合决定。
• 存在一个与材料或几何特性无关的普遍机械性能饱和水平，该水平仅由界面黏着与块体转动决定。
• TIS的最大承载能力与能量吸收受此饱和水平限制，该水平可作为理论性能基准。
• 即使在无滑移情况下，块体在界面黏着状态下的旋转能力仍限制整体结构响应，形成刚性上限。
• 通过库仑摩擦定律与桁架模型几何，可解析预测从黏着到滑移行为的转变，提供失效模式主导性的理论阈值。
• 数值模拟表明，当参数校准得当时，网格细化与罚参数对整体响应影响可忽略，证实了解的鲁棒性。