From Clausius-Duhem and Drucker-Ilyushin inequalities to standard materials

Marigo, Jean‐Jacques

doi:10.1007/0-306-46946-4_22

Cited by 9 publications

(8 citation statements)

References 7 publications

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“…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. This allowed Pham et al (2011b) to study the stability of the homogeneous response 1 of a bar whose displacements at the ends are controlled by a hard device.…”

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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“…Such energetic formulations-first introduced by Nguyen (1987Nguyen ( , 2000 and then justified by Marigo (1989Marigo ( , 2000 (see also DeSimone et al (2001)) by thermodynamical arguments for a large class of rate independent behaviors-constitute a very promising way to treat in a unified framework the questions of bifurcation and stability of solutions to quasi-static evolution problems. After the pioneering papers by Marigo (1993, 1998), Mielke (2005) formalized these concepts for the very broad class of rate independent evolution laws, Bourdin et al (2008) developed this approach in Fracture Mechanics, and Pham and Marigo (2010a,b) in Damage Mechanics.…”

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confidence: 99%

From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models

Pham

Marigo

2011

Continuum Mech. Thermodyn.

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. From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models. Continuum Mechanics and Thermodynamics, Springer Verlag, 2013, 25 (2-4), pp.147-171. 10.1007/s00161-011-0228-3. hal-00647860To be submitted to Continuum Mechanics and Thermodynamics Abstract We propose a construction method of non homogeneous solutions for the traction problem of an elastic damaging bar. This bar has a softening behavior which obeys a gradient damaged model. The method is applicable for a wide range of brittle materials. For sufficiently long bars, we show that localization arises on sets whose length is proportional to the material internal length and with a profile which is also a material characteristic. From its onset until the rupture, the damage profile is obtained either in a closed form or after a simple numerical integration depending on the model. Thus, the proposed method provides definitions for the critical stress and fracture energy that can be compared with experimental results. We finally discuss some features of the global behavior of the bar such as the possibility of a snap-back at the onset of damage. We point out the sensitivity of the responses to the parameters of the damage law. All these theoretical considerations are illustrated by numerical examples.

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“…In isothermal process, like those we are interested in, the entropy flux depends exclusively on damage. 8 In brittle damaging materials in the sense of Marigo (2000) the condition that the damage parameter should be a not decreasing function of time during damage evolution is one of the request for the Drucker-Ilyushin stability postulate be valid.…”

Section: Multifield Description Of Damage Distribution and Evolution mentioning

confidence: 99%

Uniqueness and minimum theorems for a multifield model of brittle solids

Mosconi

2006

International Journal of Solids and Structures

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From Clausius-Duhem and Drucker-Ilyushin inequalities to standard materials

Cited by 9 publications

References 7 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 the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models

Uniqueness and minimum theorems for a multifield model of brittle solids

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