From diffuse to localised damage through elastic interaction

Amitrano, David; Grasso, Jean‐Robert; Hantz, Didier

doi:10.1029/1999gl900388

Cited by 111 publications

(150 citation statements)

References 17 publications

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“…σ N min < 0 and σ N max > 0 are the maximal tensile stress and the maximal compressive stress, respectively. The friction coefficient µ for sea ice is chosen equal to 0.7, which is a common value for geo-materials (Amitrano et al, 1999) and seems to be scale-independent (Weiss and Schulson, 2009). The values of the cohesion c, σ N min , and σ N max seem to be inversely proportional to the square root of the spatial scale (Weiss et al, 2007).…”

Section: Dynamical Componentmentioning

confidence: 99%

neXtSIM: a new Lagrangian sea ice model

et al. 2016

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Abstract. The Arctic sea ice cover has changed drastically over the last decades. Associated with these changes is a shift in dynamical regime seen by an increase of extreme fracturing events and an acceleration of sea ice drift. The highly non-linear dynamical response of sea ice to external forcing makes modelling these changes and the future evolution of Arctic sea ice a challenge for current models. It is, however, increasingly important that this challenge be better met, both because of the important role of sea ice in the climate system and because of the steady increase of industrial operations in the Arctic. In this paper we present a new dynamical/thermodynamical sea ice model called neXtSIM that is designed to address this challenge. neXtSIM is a continuous and fully Lagrangian model, whose momentum equation is discretised with the finite-element method. In this model, sea ice physics are driven by the combination of two core components: a model for sea ice dynamics built on a mechanical framework using an elasto-brittle rheology, and a model for sea ice thermodynamics providing damage healing for the mechanical framework. The evaluation of the model performance for the Arctic is presented for the period September 2007 to October 2008 and shows that observed multiscale statistical properties of sea ice drift and deformation are well captured as well as the seasonal cycles of ice volume, area, and extent. These results show that neXtSIM is an appropriate tool for simulating sea ice over a wide range of spatial and temporal scales.

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Section: Dynamical Componentmentioning

confidence: 99%

neXtSIM: a new Lagrangian sea ice model

et al. 2016

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“…Space distributions (D-value) of both seismic arcs show similar values of 1.9 and 2.0; both present typical energetic power-law distributions, with a classical b-value of 1 for the Briançonnais arc and a significantly lower b-value of 0.7 for the Piedmont arc. After comparison with mechanical models (Amitrano et al 1999), these variations of energetic distributions have been interpreted in terms of ductility versus brittleness. The Briançonnais seismic arc would present a globally more brittle behavior compared to the more ductile Piedmont seismic arc.…”

Section: Comparative Analysismentioning

confidence: 99%

Extensional neotectonics around the bend of the Western/Central Alps: an overview

Sue

Delacou

Champagnac

et al. 2007

Int J Earth Sci (Geol Rundsch)

126

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The Western Alps' active tectonics is characterized by ongoing widespread extension in the highest parts of the belt and transpressive/compressive tectonics along its borders. We examine these contrasting tectonic regimes using a multidisciplinary approach including seismotectonics, numerical modeling, GPS, morphotectonics, fieldwork, and brittle deformation analysis. Extension appears to be the dominant process in the present-day tectonic activity in the Western Alps, affecting its internal areas all along the arc. Shortening, in contrast, is limited to small areas located along at the outer borders of the chain. Strike-slip is observed throughout the Alpine realm and in the foreland. The stress-orientation pattern is radial for r3 in the inner, extensional zones, and for r1 in the outer, transcurrent/tranpressional ones. Extensional areas can be correlated with the parts of the belt with the thickest crust. Quantification of seismic strain in tectonically homogeneous areas shows that only 10-20% of the geodesy-documented deformation can be explained by the Alpine seismicity. We propose that, Alpine active tectonics are ruled by isostasy/buoyancy forces rather than the ongoing shortening along the Alpine Europe/Adria collision zone. This interpretation is corroborated by numerical modeling. The Neogene extensional structures in the Alps formed under increasingly brittle conditions. A synthesis of paleostress tensors for the internal parts of the West-Alpine Arc documents major orogen-parallel extension with a continuous change in r3 directions from ENE-WSW in the Simplon area, to N-S in the Vanoise area and to NNW-SSE in the Briançon area. Minor orogen-perpendicular extension increases from N to S. This second signal correlates with the present-day geodynamics as revealed by focal-plane mechanisms analysis. The orogen-parallel extension could be related to the opening of the Ligurian Sea during the Early-Middle Miocene and to compression/ rotation of the Adriatic indenter inducing lateral extrusion.

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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.…”

mentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

“…The model, described in more details elsewhere [13,14], considers a continuous 2D elastic material (Hooke's law) under plane stress, with progressive local damage. Damage is represented by a reduction of the isotropic elastic modulus Y i of the element i, Y i (n + 1) = Y i (n)d 0 with d 0 = 0.9, each time the stress state on that element exceeds a given threshold.…”

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confidence: 99%

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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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From diffuse to localised damage through elastic interaction

Cited by 111 publications

References 17 publications

neXtSIM: a new Lagrangian sea ice model

neXtSIM: a new Lagrangian sea ice model

Extensional neotectonics around the bend of the Western/Central Alps: an overview

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

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