Approche globale, minima relatifs et Critère d'Amorçage en Mécanique de la Rupture

Laverne, Jérôme; Marigo, Jean‐Jacques

doi:10.1016/j.crme.2004.01.014

Cited by 15 publications

(6 citation statements)

References 2 publications

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“…Therefore, it has become necessary to introduce additional criteria to select physically realistic solutions. In the spirit of Nguyen (2000), recent variational approaches (Charlotte et al 2000;Laverne and Marigo 2004;Mielke 2005;Charlotte et al 2006;Bourdin et al 2008) propose to reinforce usual stationary conditions with a stability condition. Making a full use of the justification of such an energetic approach given by Marigo (1989Marigo ( , 2000, see also DeSimone et al (2001), Pham and Marigo (2010a,b) introduced this stability criterion as one of the three principles (along with irreversibility and energy balance) that governs the evolution of damage in a body.…”

Section: Introductionmentioning

confidence: 99%

Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting

Pham

Marigo

2012

J Elast

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Considering a family of gradient-enhanced damage models and taking advantage of its variational formulation, we study the stability of homogeneous states in a full three-dimensional context. We show that gradient terms have a stabilizing effect, but also how those terms induce structural effects. We emphasize the great importance of the type of boundary conditions, the size and the shape of the body on the stability properties of such states.

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Section: Introductionmentioning

confidence: 99%

Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting

Pham

Marigo

2012

J Elast

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“…In itself, FFM does not reduce to a criterion on stress in the absence of stress concentration. To capture yield failure, the variational approach of Francfort and Marigo (1998) has been combined with cohesive zone interfaces instead of a Griffith (infinitely thin) surface (Laverne and Marigo, 2004;Charlotte et al, 2006;Bourdin et al, 2008), thus offering a more general application of CZM since the path of initiated crack is no more needed a priori. Another approach has been proposed by Leguillon (2002) to capture yield failure in FFM, the application of which is simpler than cohezive zone interfaces since it relies on a linear elastic calculation only: failure occurs if the energy criterion of FFM is satisfied and if the yield failure criterion is verified along the path of the initiated finite crack.…”

Section: Theories Of Initiationmentioning

confidence: 99%

From yield to fracture, failure initiation captured by molecular simulation

Brochard

Tejada

Sab

2016

Journal of the Mechanics and Physics of Solids

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International audienceWhile failure of cracked bodies with strong stress concentrations is described by an energy criterion (fracture mechanics), failure of flawless bodies with uniform stresses is captured by a criterion on stress (yielding). In-between those two cases, the problem of failure initiation from flaws that moderately concentrate stresses is debated. In this paper, we propose an investigation of the process of failure initiation at the atomic scale by means of molecular simulations. We first discuss the appropriate scaling conditions to capture initiation, since system sizes that can be simulated by molecular mechanics are strongly limited. Then, we perform a series of molecular simulations of failure of a 2D model material, which exhibits strength and toughness properties that are suitable to capture initiation with systems of reasonable sizes. Transition from fracture failure to yield failure is well characterized. Interestingly, in some specific cases, failure exceeds yield failure which is in contradiction with most initiation theories. This occurs when stress are highly concentrated while little mechanical energy is stored in the material. This observation calls for a theory of initiation which requires that both stress and energy are necessary conditions of failure. Such an approach was proposed by Leguillon (2002). We show that the predictions of this theory are consistent with the molecular simulation results

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“…This result can be extended to a general three-dimensional setting via the same stability criterion. In particular, assuming that the material is isotropic and hence that the surface energy density is only a function of the normal displacement jump and of the norm of the tangential displacement jump across the crack lips, i.e., Φ(JuK • n, JuK − (JuK • n) n ), where n denotes the local unit normal vector to the crack, it is stated in [23] and proved in [9] that the crack nucleation criterion takes the form of an intrinsic curve in the Mohr stress plane which involves the directional derivatives at (0, 0) of Φ. Furthermore, when Φ admits partial derivatives at (0, 0), the nucleation criterion simply reduces to the two usual criteria of maximal shear stress and maximal tensile stress.…”

Section: 2mentioning

confidence: 99%

Stress gradient effects on the nucleation and propagation of cohesive cracks

Pham¹,

Laverne²,

Marigo³

2016

DCDS-S

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International audienceThe aim of the present work is to study the nucleation and propagation of cohesive cracks in two-dimensional elastic structures. The crack evolution is governed by Dugdale’s cohesive force model. Specifically, we investigate the stabilizing effect of the stress field non-uniformity by introducing a length l which characterizes the stress gradient in a neighborhood of the point where the crack nucleates. We distinguish two stages in the crack evolution: the first one where the entire crack is submitted to cohesive forces, followed by a second one where a non-cohesive part appears. Assuming that the material characteristic length dc associated with Dugdale’s model is small in comparison with the dimension L of the body, we develop a two-scale approach and, using the methods of complex analysis, obtain the entire crack evolution with the loading in closed form. In particular, we show that the propagation is stable during the first stage, but becomes unstable with a brutal crack length jump as soon as the non-cohesive crack part appears. We also discuss the influence of the problem parameters and study the sensitivity to imperfections

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Approche globale, minima relatifs et Critère d'Amorçage en Mécanique de la Rupture

Cited by 15 publications

References 2 publications

Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting

Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting

From yield to fracture, failure initiation captured by molecular simulation

Stress gradient effects on the nucleation and propagation of cohesive cracks

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