Statistical properties of fracture in a random spring model

Nukala, Phani K. V. V.; Zapperi, Stefano; Šimunović, Srđan

doi:10.1103/physreve.71.066106

Cited by 60 publications

(43 citation statements)

References 22 publications

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“…The RSM is similar to the RFM, but the fuses are replaced by elastic springs that break when their elongation reaches a random threshold. While the RSM represents more faithfully the elastic continuum, the statistical properties of the fracture process are analogous to those of the RFM [14].…”

Section: Prl 100 055502 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

“…Damage accumulates until a connected fracture path disconnects the network and one can define the strength c as the total peak current divided by the length of the bus bar. We also perform numerical simulations for the random spring model (RSM) [14], similar to the mesoscale models used routinely for concrete [15]. The RSM is similar to the RFM, but the fuses are replaced by elastic springs that break when their elongation reaches a random threshold.…”

Section: Prl 100 055502 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

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Role of Disorder in the Size Scaling of Material Strength

2008

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We study the sample size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the fluctuations due to disorder and another controlled by stress-concentrations, ruled by continuum fracture mechanics. The results are formulated in terms of a scaling law involving a statistical fracture process zone. Its existence and scaling properties are only revealed by sampling over many configurations of the disorder. The scaling law is in good agreement with experimental results obtained from notched paper samples.

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Section: Prl 100 055502 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Section: Prl 100 055502 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Role of Disorder in the Size Scaling of Material Strength

2008

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“…In the limit of infinitely strong disorder, fracture can be mapped onto the percolation problem [10], suggesting a critical transition. This interpretation remains however controversial in the case of non-infinite disorder, as lattice models show an abrupt localization of damage at failure, without a diverging correlation length, arguing instead for a first-order transition [9,11,12].In this letter, we revisit these problems for compressive failure of an heterogeneous material with variable range of disorder, on the basis of a continuous progressive damage model [13,14]. This model is more realistic than lattice models or scalar damage models [15], as it explicitely accounts for the tensorial nature of stresses and strains.…”

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confidence: 99%

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confidence: 99%

Damage-Cluster Distributions and Size Effect on Strength in Compressive Failure

2012

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We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure of brittle materials like rocks or ice. We show that the size distribution of damage-clusters, as well as the evolution of an order parameter, the size of the largest damage-cluster, argue for a critical interpretation of fracture. The compressive failure strength follows a normal distribution with a very small size effect on the mean strength, in good agreement with experiments.Understanding how materials break is a fundamental problem that has both theoretical and practical relevance. The topic has received considerable renewed attention during the last few decades because of the limitations of the classical Griffith theory for heterogeneous media [1][2][3]. The practical applications are numerous, from material and structural design, to the important problem of size effects on strength (e.g. [4]). The two key components that make material failure challenging to understand are long-range interactions and material disorder.Traditionally, Weibull and Gumbel distributions associated with the weakest-link approach have been widely used to describe the strength of brittle materials. These distributions naturally arise from extreme-value statistics of initial defect distributions based on the assumptions that [5] (i) defects do not interact with one another, (ii) failure of the whole system is dictated by the activation of the largest flaw (the weakest-link hypothesis), and finally (iii) the material strength can be related to the critical defect size. These assumptions are reasonable for materials with relatively weak disorder loaded under tension, but do not hold for heterogeneous materials with broad distribution of initial disorder or for loading conditions stabilizing crack propagation, such as compression. In these cases there is experimental evidence that a considerable amount of damage can be sustained before failure [6]. Under these conditions, failure is the culmination of a complex process involving the nucleation, propagation, interaction and coalescence of many microcracks [7]. Stress states observed under various natural conditions, ranging from soil and rock mechanics to earthquake physics, suggest the importance of compressive failure.A cornerstone for the understanding of breakdown of disordered media has been lattice models of fracture in * lucas.girard@geo.uzh.ch which networks with prescribed bond failure thresholds are subject to increasing external loads [2]. In these models, failure is described on a qualitative level as the interplay between disorder and elasticity. When strong disorder is considered, these models suggest that fracture strength does indeed not follow a Weibull or a Gumbel distribution but a log-normal distribution [8,9]. Similar strength distributions have been obtained for different model types (fuses and springs), in 2D and 3D, suggesting ...

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“…[1][2][3][4][5][6][7][8] A representative tough biomaterial, pearl or nacre, has been studied extensively. Various approaches to understanding the toughening mechanisms have been proposed, [9][10][11][12][13][14][15][16][17] and they have inspired a number of useful applications. [18][19][20][21] In the tough and strong layer, the cuticle, in the exoskeleton of lobsters, bundles of chitin-protein fibers are embedded in a calcium carbonate matrix (Fig.…”

Section: Introductionmentioning

confidence: 99%

Simple Model for the Toughness of a Helical Structure Inspired by the Exoskeleton of Lobsters

Okumura

2013

J. Phys. Soc. Jpn.

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Nature has evolved remarkable hierarchical structures to realize tough biocomposites. The helical structure of the exoskeleton generally found in crustaceans is one such example. Recently, detailed structural and mechanical properties of the exoskeleton have been actively studied for lobsters, which has inspired artificial biomineralization. However, the superiority of the special structure giving the toughness has yet to be elucidated. Here, we develop a simple model of the structure of crustaceans via two-step coarse-graining to obtain a scaling law for fracture energy, a measure of fracture toughness. The law provides a clear physical understanding of how the simple model structure is optimized in terms of its the toughness by exploiting at least five important design principles.

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Statistical properties of fracture in a random spring model

Cited by 60 publications

References 22 publications

Role of Disorder in the Size Scaling of Material Strength

Role of Disorder in the Size Scaling of Material Strength

Damage-Cluster Distributions and Size Effect on Strength in Compressive Failure

Simple Model for the Toughness of a Helical Structure Inspired by the Exoskeleton of Lobsters

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