  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.
