Aggregate interlocking allows transferring shear and normal stresses through open cracks, and is considered to significantly contribute to the force transfer in cracked concrete. The complex phenomenon depends on the roughness of cracked surfaces, where material protruding from one side may engage with the opposite one. Two-Phase models were established in the 1980's by Walraven to estimate the force transfer, distinguishing between cement matrix and spherical aggregates. The approach leads to good results but has several shortcomings. In this paper, the fundamental assumptions are reviewed using specific numerical and experimental investigations. Special tests respecting the geometrical assumptions are presented and the results compared with numerically calculated estimates. The model is extended to address some shortcomings and investigate the physical nature of the main parameters. Positive aspects of Two-Phase Models and a number of limitations are highlighted, allowing a consistent step forward in the understanding of aggregate interlocking.
In materials, the evolution of crack surfaces is intimately linked with the self-contact occurring between them. The developed contact forces not only mitigate the effect of stress concentration at crack tip but also contribute significantly to the transfer of shear and normal stresses. In this article, we present a numerical framework to study the simultaneous process of fracture and self-contact between fracturing surfaces. The widely used approach, where contact constraints are enforced with the cohesive element traction separation law, is demonstrated to fail for relative displacements greater than the characteristic mesh length. A hybrid approach is proposed, which couples a node-to-segment contact algorithm with extrinsic cohesive elements. Thus, the fracture process is modeled with cohesive elements, whereas the contact and the friction constraints are enforced through a penalty-based method. This hybrid cohesive-contact approach is shown to alleviate any mesh topology limitations, making it a reliable and physically based numerical model for studying crack propagation along rough surfaces.
In concrete structures, opened cracks contribute significantly to the transfer of shear and normal stresses through the contact forces occurring between fractured surfaces. Such contact forces are due to protruding asperities, engaged by interlocking and friction. In this paper, the role played by roughness on shear resistance is investigated numerically. First, micro computed tomography and digital microscope measures of concrete surfaces are used to validate a novel numerical generator of realistic cracked concrete surfaces. Secondly, a contact solver based on the boundary integral approach allows an extremely fine description of typical cracked surface topologies. Roughness changes drastically the predictions, so that the shear resistance computed numerically matches the prior experimental results reported in the literature. The proposed model does not need any fitting procedure, making it a reliable and physically based method for predicting shear transfer phenomena in concrete. An empirical power-law predicting the shear resistance in concrete is a direct outcome, which accounts for micro-scale roughness and aggregate distribution.
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.
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