Self-consistent scheme for toughness homogenization

Roux, Stéphane; Hild, François

doi:10.1007/s10704-008-9271-x

Cited by 10 publications

(11 citation statements)

References 22 publications

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“…Fig.7-B shows the PDF of E dep for experiment I at strain S b when an avalanche is triggered. This energy is sometimes called the depinning energy, and in the framework of the pinning-depinning theory, several models predict Gaussian statistics [47][48][49][50]. In our case, unlike these models, we observe a power-law distribution, and the measured experimental exponent is close to 1: γ = −1.08 ± 0.1.…”

Section: A Global Avalanchessupporting

confidence: 39%

Local and global avalanches in a two-dimensional sheared granular medium

Barés

Wang

et al. 2017

Phys. Rev. E

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We present the experimental and numerical studies of a 2D sheared amorphous material constituted of bidisperse photo-elastic disks. We analyze the statistics of avalanches during shear including the local and global fluctuations in energy and changes in particle positions and orientations. We find scale free distributions for these global and local avalanches denoted by power-laws whose cutoffs vary with inter-particle friction and packing fraction. Different exponents are found for these power-laws depending on the quantity from which variations are extracted. An asymmetry in time of the avalanche shapes is evidenced along with the fact that avalanches are mainly triggered from the shear bands. A simple relation independent from the intensity, is found between the number of local avalanches and the global avalanches they form. We also compare these experimental and numerical results for both local and global fluctuations to predictions from meanfield and depinning theories.

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Section: A Global Avalanchessupporting

confidence: 39%

Local and global avalanches in a two-dimensional sheared granular medium

Barés

Wang

et al. 2017

Phys. Rev. E

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“…Heterogeneities of fracture energy in 3D brittle materials have been shown to lead to similar instabilities, producing the so-called crackling noise [7,17,18]. This effect was shown to increase considerably the macroscopic fracture energy of brittle disordered materials [19,20].…”

Section: (B) As a Function Of The Level Of Heterogeneity Dsmentioning

confidence: 99%

Toughening and Asymmetry in Peeling of Heterogeneous Adhesives

et al. 2012

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The effective adhesive properties of heterogeneous thin films are characterized through a combined experimental and theoretical investigation. By bridging scales, we show how variations of elastic or adhesive properties at the microscale can significantly affect the effective peeling behavior of the adhesive at the macroscale. Our study reveals three elementary mechanisms in heterogeneous systems involving front propagation: (i) patterning the elastic bending stiffness of the film produces fluctuations of the driving force resulting in dramatically enhanced resistance to peeling; (ii) optimized arrangements of pinning sites with large adhesion energy are shown to control the effective system resistance, allowing the design of highly anisotropic and asymmetric adhesives; (iii) heterogeneities of both types result in front motion instabilities producing sudden energy releases that increase the overall adhesion energy. These findings open potentially new avenues for the design of thin films with improved adhesion properties, and motivate new investigation of other phenomena involving front propagation.PACS numbers: 62.20. Mk, 46.50.+a, 68.35.Ct Bridging microscale properties of materials with their effective mechanical behavior at the macroscale is a major challenge in both pure and applied science. A great deal of research effort has been dedicated to the study of effective elastic properties in heterogeneous systems. Composite materials, structures and meta-materials can achieve extraordinary effective properties, e. g. negative Poisson's ratio [1] or stiffness greater than diamond [2], and elegant homogenization techniques have been developed in order to efficiently link micro to macroscale in elastic settings [3][4][5]. Surprisingly, our understanding of the role of heterogeneities on the overall resistance of these systems to failure resulting from the propagation of free boundaries and free discontinuities is rather limited, despite the major importance of this question in engineering science. For example, stress concentration generated by brittle cracks makes the macroscopic system extremely sensitive to microscopic features -the scale invariant roughening of cracks as well as their highly intermittent dynamics are good illustrations of this effect [6,7] -raising fundamental impediments to the development of reliable homogenization techniques for fracture problems.In this letter, we address the challenge of finding the macroscopic resistance to front propagation in a heterogeneous media in the context of thin film peeling. There has been a recent renewal of interest in adhesive systems driven by the exploration of exceptional properties of biological systems like geckos. Consequently, much attention has focused on adhesion enhancement achieved by 3D features of the adhesive surface, such as arrays of fibrils [8,9] or hierarchical structures [10]. Here, we will show that such a rather complex microstructure is not required to achieve enhanced adhesion: heterogeneities in the elastic properties of the film ...

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“…Unfortunately this approach gives the critical force only up to a numerical prefactor, whose value depends on microscopic quantities such as the geometrical shape of the impurities, and which is essential to determine in view of applications. Recently, a numerical self-consistent scheme [22,23] and numerical simulations have focused on a precise determination of the critical force [24,25] in the context of brittle failure. Notably, is has been shown that in the collective regime, occurring at weak disorder amplitude, the critical force does not depend on the disorder distribution but only on the disorder amplitude and correlation length [24].…”

Section: Introductionmentioning

confidence: 99%

The effect of disorder geometry on the critical force in disordered elastic systems

Démery¹,

Lecomte²,

Rosso³

2014

J. Stat. Mech.

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Abstract. We address the effect of disorder geometry on the critical force in disordered elastic systems. We focus on the model system of a long-range elastic line driven in a random landscape. In the collective pinning regime, we compute the critical force perturbatively. Not only our expression for the critical force confirms previous results on its scaling with respect to the microscopic disorder parameters, it also provides its precise dependence on the disorder geometry (represented by the disorder two-point correlation function). Our results are successfully compared to the results of numerical simulations for random field and random bond disorders.

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Self-consistent scheme for toughness homogenization

Cited by 10 publications

References 22 publications

Local and global avalanches in a two-dimensional sheared granular medium

Local and global avalanches in a two-dimensional sheared granular medium

Toughening and Asymmetry in Peeling of Heterogeneous Adhesives

The effect of disorder geometry on the critical force in disordered elastic systems

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