Betweenness centrality as predictor for forces in granular packings

Kollmer, Jonathan E.; Daniels, Karen E.

doi:10.1039/c8sm01372a

Cited by 40 publications

(41 citation statements)

References 56 publications

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“…We aim to use our insight into the force network to investigate the physical mechanisms that drive nonlocal effects in experiments at low-intermediate values of I where such non-local effects are becoming relevant. In addition, we test whether the shear rate is an appropriate variable in the description of fluidity at all, given that even for static granular packings, force chain configurations are not solely determined by particle positions 36,37 . Instead, there is a force network ensemble (FNE) which can fluctuate independent of, and in addition to, particle rearrangements under shear.…”

Section: Introductionmentioning

confidence: 99%

Force fluctuations at the transition from quasi-static to inertial granular flow

et al. 2019

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Section: Introductionmentioning

confidence: 99%

Force fluctuations at the transition from quasi-static to inertial granular flow

et al. 2019

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“…For example, while their shear modulus vanishes at the jamming point, their bulk modulus remains finite [30], which is rather different from, for example, central-force spring networks where both the bulk and shear modulus vanish at their equivalent jamming point [32]. Our networks are generated from real, frictional packings [35] drawn from experiments on uniaxially compressed quasi-2D bidisperse granular packings of frictional photoelastic disks, created using the techniques described in [28,[36][37][38]. In each case, the test structure has a geometry defined by the binary contact network of these disks.…”

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confidence: 99%

Rigidity percolation control of the brittle-ductile transition in disordered networks

Berthier

Kollmer

Henkes

et al. 2019

Phys. Rev. Materials

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In ordinary solids, material disorder is known to increase the size of the process zone in which stress concentrates at the crack tip, causing a transition from localized to diffuse failure. Here, we report experiments on disordered 2D lattices, derived from frictional particle packings, in which the mean coordination number z of the underlying network provides a similar control. Our experiments show that tuning the connectivity of the network provides access to a range of behaviors from brittle to ductile failure. We elucidate the cooperative origins of this transition using a frictional pebble game algorithm on the original, intact lattices. We find that the transition corresponds to the isostatic value z = 3 in the large-friction limit, with brittle failure occurring for structures vertically spanned by a rigid cluster, and ductile failure for floppy networks containing nonspanning rigid clusters. Furthermore, we find that individual failure events typically occur within the floppy regions separated by the rigid clusters. Materials as varied as semiconductors [1], aqueous foams [2], polymers [3], metals [4] and rocks[5] exhibit a brittle-ductile transition when parameters such as geometry, temperature, pressure, loading rate, or even illumination are varied. Because brittle failure occurs suddenly and unpredictably, often leading to catastrophic effects, it is important to understand which underlying control parameters are able to tune the failure behavior of materials and structures, including those that are heterogeneous and/or hierarchical. Improvements in the prediction of failure modes are essential to the design of optimal properties.Controlled studies of the brittle-ductile transition have been achieved both numerically and experimentally. For example, increasing material disorder has been shown [6-10] to increase the fracture process zone (FPZ) size, resulting in a less concentrated stress at the crick tip. The size of the FPZ eventually diverges for infinite disorder, producing a transition from a brittle narrow crack type failure to percolation-like diffuse behavior. Experimentally, Hanifpour et al. [11] showed that 3D-printed disordered auxetic lattices can fail in a ductile or brittle (with disorder-dependent tensile strength) manner depending on the loading direction. Driscoll et al. [12] demonstrated the key role of material rigidity in experiments on weakly-disordered honeycomb acrylic lattices, and also the key role of connectivity in numerical studies of two different types of spring networks, one of which was derived from numerical realizations of frictionless packings. Numerical studies in Zhang et al.[13], on the other hand, focused on how the nonlinear alignment of springs in a randomly diluted triangular lattice controls the transition at connectivities below what is known as the central force rigidity percolation point. Finally, Bouzid and Del Gado [14] focused on the role of connectivity in a disordered system, by studying the mechanical * corresponding author: Estelle Berthier (ehber...

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“…Combined with [36,37], our work provides evidence that betweenness centrality successfully identifies physical properties in both granular packings and lattices that are derived from them. Similarly, analyses inspired by rigidity percolation in granular materials have identified that our disordered lattices undergo a ductile-brittle failure transition as a function of connectivity z 0 , as determined by counting degrees of freedom and constraints [38].…”

Section: Discussionmentioning

confidence: 84%

Forecasting failure locations in 2-dimensional disordered lattices

Berthier

Porter

Daniels

2019

Proc. Natl. Acad. Sci. U.S.A.

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Forecasting fracture locations in a progressively failing disordered structure is of paramount importance when considering structural materials. We explore this issue for gradual deterioration via beam breakage of two-dimensional disordered lattices, which we represent as networks, for various values of mean degree. We study experimental samples with geometric structures that we construct based on observed contact networks in 2D granular media. We calculate geodesic edge betweenness centrality, which helps quantify which edges are on many shortest paths in a network, to forecast the failure locations. We demonstrate for the tested samples that, for a variety of failure behaviors, failures occur predominantly at locations that have larger geodesic edge betweenness values than the mean one in the structure. Because only a small fraction of edges have values above the mean, this is a relevant diagnostic to assess failure locations. Our results demonstrate that one can consider only specific parts of a system as likely failure locations and that, with reasonable success, one can assess possible failure locations of a structure without needing to study its detailed energetic states. arXiv:1812.08025v3 [cond-mat.soft]

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Betweenness centrality as predictor for forces in granular packings

Cited by 40 publications

References 56 publications

Force fluctuations at the transition from quasi-static to inertial granular flow

Force fluctuations at the transition from quasi-static to inertial granular flow

Rigidity percolation control of the brittle-ductile transition in disordered networks

Forecasting failure locations in 2-dimensional disordered lattices

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