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结构体系，在多功能工程应用中展现出广阔前景。研究表明，这类结构具有超越传统工程材料的优异力学性能，包括刚度、强度与韧性的出色协同。近期研究建立了梁状拓扑互锁结构的强度与韧性理论上限，但该极限仅能在摩擦系数极高的理想化结构中实现，因此其在真实结构中的可实现性尚不明确。本文受生物系统启发，提出一种层级式拓扑互锁方法，突破了上述限制，为力学性能优化提供了新路径。我们研究了具有可控振幅与波长的正弦表面形貌的梁状拓扑互锁结构，并通过数值模拟分析其力学特性。结果表明，表面形貌可增强界面有效摩擦强度，经优化设计后，使用实际摩擦系数即可达到结构承载力的理论极限。此外，我们发现界面有效摩擦系数与表面形貌的关系可由结合表面曲率与梯度的准则精确描述。本研究证明了通过表面形貌构筑可显著提升梁状拓扑互锁结构力学性能的潜力。