On the failure of beam-like topologically interlocked structures

TL;DR

This paper investigates the failure mechanisms of beam-like topologically interlocked structures, analyzing how interface friction, geometry, and material properties influence whether they fail by slip or stick, and establishes an upper bound for their performance.

Contribution

It combines analytical and computational methods to identify the dominant failure mechanisms and provides a theoretical upper bound for the structural response based on interface and geometric parameters.

Findings

Friction coefficient and height control slip or stick failure modes.

Sticking mechanism and block rotation set a performance saturation level.

Provides a theoretical benchmark for maximum structural response.

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.