Topologically interlocked materials and structures, which are assemblies of unbonded interlocking building blocks, are promising concepts for versatile structural applications. They have been shown to exhibit exceptional mechanical properties, including outstanding combinations of stiffness, strength, and toughness, beyond those achievable with common engineering materials. Recent work has established a theoretical upper limit for the strength and toughness of beam-like topologically interlocked structures. However, this theoretical limit is only achievable for structures with unrealistically high friction coefficients; therefore, it remains unknown whether it is achievable in actual structures. Here, we demonstrate that a hierarchical approach for topological interlocking, inspired by biological systems, overcomes these limitations and provides a path toward optimized mechanical performance. We consider beam-like topologically interlocked structures that present a sinusoidal surface morphology with controllable amplitude and wavelength and examine the properties of the structures using numerical simulations. The results show that the presence of surface morphologies increases the effective frictional strength of the interfaces and, if well-designed, enables us to reach the theoretical limit of the structural carrying capacity with realistic friction coefficients. Furthermore, we observe that the contribution of the surface morphology to the effective friction coefficient of the interface is well described by a criterion combining the surface curvature and surface gradient. Our study demonstrates the ability to architecture the surface morphology in beam-like topological interlocked structures to significantly enhance its structural performance.

翻译：拓扑互锁材料与结构是由无粘结互锁构件组装而成的概念，在多功能结构应用中展现出广阔前景。研究表明，此类结构具有卓越的力学性能，包括超越传统工程材料的刚度、强度与韧性的优异组合。近期研究已建立了梁式拓扑互锁结构强度与韧性的理论上限，但该理论极限仅能在摩擦系数极高的非现实条件下达到，因此其在实际结构中的可行性尚未明确。本文受生物系统启发，提出一种层级拓扑互锁方法，克服了上述局限，为优化力学性能提供了可行路径。我们研究了具有可控振幅与波长的正弦表面形貌的梁式拓扑互锁结构，并通过数值模拟分析其特性。结果表明，表面形貌的存在增强了界面有效摩擦强度，若设计得当，可在实际摩擦系数下接近结构承载能力的理论极限。此外，我们观察到表面形貌对界面有效摩擦系数的贡献可通过结合表面曲率与表面梯度的准则进行精确描述。本研究展示了通过构型化表面形貌显著提升梁式拓扑互锁结构力学性能的可行性。