  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.
