The random fuse network as a model of rupture in a disordered medium

Gilabert, A.; Vanneste, Christian; Sornette, Didier; Guyon, E.

doi:10.1051/jphys:01987004805076300

Cited by 46 publications

(30 citation statements)

References 9 publications

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“…Furthermore, such discrete structures have been commonly used in statistical models of fracture [20], as a means to conveniently discretize a material. For example, the random fuse model (RFM) [7,21,22], fiber bundle model (FBM) [23,24] or elastic springs model [7,9,13,25,26] descriptions rely on such lattices in which material disorder is introduced. Despite a wealth of models, few fracture experiments to discriminate between the various models have been performed on disordered lattices [11,12], in part due to the difficulty of creating samples by hand [22].With the advent of laser-cutting technology, we are able to readily produce samples with precise, reproducible properties and thereby perform controlled experiments on the failure behavior of disordered lattices with various connectivities.…”

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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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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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“…This relation gives the respective theoretical values x D 1:8 for 2D systems and x D 1:35 for 3D systems. However, numerical simulations on random 2D fuse networks [7] gave the value x D 0:82 in disagreement with the theoretical value, but in fair agreement with an independent determination [8] of z D 0:48 on similar fuse networks, recalling that in 2D percolation systems the conductivity exponent is t D 1:3.…”

Section: Methodsmentioning

confidence: 48%

Static and dynamic non-linear behaviors of carbon particle filled polymers with positive thermal coefficient

Carmona¹,

Lamaignère²

2001

Composite Interfaces

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Polymers lled with conductive particles like carbon black, short carbon bers or microbeads, may exhibit a very large positive thermal coef cient of the electrical resistance when they are heated above room temperature. Such a behavior is particularlyuseful in industrial applications for producing electrical safety devices. We present a comprehensive study of the electrical properties of epoxies lled with carbon microbeads when heating is achieved by the Joule effect. In that case, the electrical responses up to a large enough electrical excitation must be non-linear as a result of progressive heating of the material. As expected, we have found that it depends on both the 'intrinsic' properties of the sample (essentiallya function of the composition) and the extent of thermal coupling between the investigated sample and the external thermal bath (variable heat leak). We have particularly studied the stationary states under constant applied voltage and the transients following a step like time dependent voltage. Most of our ndings agree with the general results of percolation theory combined with theoretical models of rupture on a random fuse network and with a simple model of heat ow through the sample and from the sample to the thermal bath.

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“…Alternately, especially in cases where complicated patterns of quenched disorder and spatial inhomogeneity are involved, network (e.g., "random resistor" and elastic mesh) models have proved usefu1. 6 'These latter approaches are specifically suited to characterizing scaling behavior for the dependence of strength on size 7 and to describing the fractal nature of crack evolution. 8 Another challenge in the study of failure of materials is to estimate theoretically the ideal strength of a defect-free solid, and to understand how defects reduce the strength of real materials to values well below this ideal limit.…”

Section: Introductionmentioning

confidence: 99%