arXiv subjects

Shai Feldfogel

Publications and source records attributed to Shai Feldfogel.

7 recordsLinked to original sources

arXiv2023

The key to the enhanced performance of slab-like topologically interlocked structures with non-planar blocks

Topologically interlocked structures are assemblies of interlocking blocks that hold together solely through contact. Such structures have been shown to exhibit high strength, energy dissipation, and crack arrest properties. Recent studies on topologically interlocked structures have shown that both the peak strength and work-to-failure saturate with increasing friction coefficient. However, this saturated structural response is only achievable with nonphysically high values of the friction coefficient. For beam-like topologically interlocked structures, non-planar blocks provide an alternate approach to reach similar structural response with friction properties of commonly used materials. It remains unknown whether non-planar blocks have similar effects for slab-like assemblies, and what the achievable structural properties are. Here, we consider slab-like topologically interlocked structures and show, using numerical simulations, that non-planar blocks with wave-like surfaces allow for saturated response capacity of the structure with a realistic friction coefficient. We further demonstrate that non-planar morphologies cause a non-linear scaling of the work-to-failure with peak strength and result in significant improvements of the work-to-failure and ultimate deflection - values that cannot be attained with planar-faced blocks. Finally, we show that the key morphology parameter responsible for the enhanced performance of non-planar blocks with wave-like surfaces is the local angle of inclination at the hinging points of the loaded block. These findings shed new light on topologically interlocked structures with non-planar blocks, allowing for a better understanding of their strengths and energy absorption.

math.NA↗

arXiv2023

The deflection limit of slab-like topologically interlocked structures

Topologically Interlocked Structures (TIS) are structural assemblies that achieve stability and carrying capacity through the geometric arrangement of interlocking blocks, relying solely on normal and friction forces for load transfer. Unlike beam-like TIS, whose deflection never exceeds the height of the blocks, the deflection of slab-like TIS often does. Yet, the upper limit of deflection of slab-like TIS, a key parameter defining their loading energy capacity, remains unexplored. Here, we establish a theoretical upper bound for the deflection capacity of slab-like TIS and outline a systematic design strategy to approach this upper bound. This strategy is based on engineering the contact interfaces such that the non-central blocks are more engaged in the structural response, leading to a more global and holistic deformation mode with higher deflections. We demonstrate the application of this strategy in a numerical case study on a typical slab-like TIS. We show that it leads to a 350$\%$ increase in deflection, yielding a value closer to the upper bound than previously reported in the literature. We also show that the resulting deflection mode engages all the blocks equally, avoids localized sliding modes, and resembles that of monolithic equivalents. Lastly, we show that the strategy not only maximizes the assembly's deflection capacity but also its loading energy capacity.

cond-mat.soft↗

arXiv2023

Beam-like topologically interlocked structures with hierarchical interlocking

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.

math.NA↗

arXiv2022

Scaling, saturation, and upper bounds in the failure of topologically interlocked structures

Topological Interlocking Structures (TIS) have been increasingly studied in the past two decades. However, some fundamental questions concerning the effects of Young's modulus and the friction coefficient on the structural mechanics of the most common type of TIS application - centrally loaded slabs - are not yet clear. Here, we present a first-of-its-kind parametric study based on the Level-Set-Discrete-element-Method that aims to clarify how these two parameters affect multiple aspects of the behavior and failure of centrally-loaded TIS slabs. This includes the evolution of the structural response up to and including failure, the foremost structural response parameters, and the residual carrying capacity. We find that the structural response parameters in TIS slabs scale linearly with Young's modulus, that they saturate with the friction coefficient, and that the saturated response provides an upper-bound on the capacity of centrally loaded TIS slabs reported in the literature. This, together with additional findings, insights, and observations, comprise a novel contribution to our understanding of the interlocked structural form.

cond-mat.soft↗

arXiv2022

Failure of topologically interlocked structures -- a Level-Set-DEM approach

Topological Interlocking Structures (TIS) are assemblies of interlocking building blocks that hold together solely through contact and friction at the blocks' interfaces, and thus do not require any connective elements. This salient feature makes them highly energy-absorbing, resistant to crack propagation, geometrically versatile, and re-usable. It also gives rise to failure mechanisms that, differently from ordinary structures, are governed by multiple contact interactions between blocks and frictional slip at their interfaces. Commonly-used modeling tools for structural analysis severely struggle to capture and quantify these unusual failure mechanisms. Here, we propose a different approach that is well suited to model the complex failure of TIS. It is based on the Level-Set-Discrete-Element-Method, originally developed for granular mechanics applications. After introducing the basic assumptions and theoretical concepts underlying our model, we show that it well-captures experimentally observed slip-governed failure in TIS slabs and that it estimates the force-displacement curves better than presently available modeling tools. The theoretical foundation together with the results of this study provide a proof-of-concept for our new approach and point to its potential to improve our ability to model and to understand the behavior of interlocked structural forms.

cond-mat.soft↗

arXiv2022

A discretization-convergent Level-Set-DEM

The recently developed level-set-DEM is able to seamlessly handle arbitrarily shaped grains and their contacts through a discrete level-set representation of grains' volume and a node-based discretization of their bounding surfaces. Heretofore, the convergence properties of LS-DEM with refinement of these discretizations have not been examined. Here, we examine these properties and show that the original LS-DEM diverges upon surface discretization refinement due to its force-based discrete contact formulation. Next, we fix this issue by adopting a continuum-based contact formulation wherein the contact interactions are traction-based, and show that the adapted LS-DEM is fully discretization convergent. Lastly, we discuss the significance of convergence in capturing the physical response, as well as a few other convergence-related topics of practical importance.

math.NA↗

arXiv2022

On the failure of beam-like topologically interlocked structures

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.

math.NA↗