Jean-Jacques Marigo

Bifurcation and stability issues in gradient theories with softening

A bifurcation and stability analysis is carried out here for a bar made of a material obeying a gradient damage model with softening. We show that the associated initial boundary-value problem is ill posed and one should expect mesh sensitivity in numerical solutions. However, in contrast to what happens for the underlying local damage model, the damage localization zone has a finite thickness and stability arguments can help in the selection of solutions.

A damage mechanics approach to stress softening and its application to rubber

Abstract We analyze stress softening phenomena within the framework of the ‘generalized standard material’ based on the notion of a ‘normal dissipative mechanism’. We prove that the monotonicity properties of the ‘yield function’ governing such mechanism lead to local and global uniqueness of the response. Applications to oscillators with a single degree of freedom, whose anharmonic spring exhibits stress softening, are also presented.

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

We study the power of restriction of Clausius-Duhem and Drucker-Ilyushin inequalities on the constitutive relations of several classes of materials, such as elastic, elastoplastic, brittle damaging and viscous ones. The goal is to see whether these two physical principles can justify the very useful but formal notion of standard materials.

The taming of plastic slips in von Mises elasto-plasticity

We derive sufficient conditions that prevent the formation of plastic slips in three-dimensional small strain Prandtl-Reuss elasto-plasticity when the yield criterion is of the Von Mises type.

Vers une théorie énergétique de la rupture fragile

The drawbacks of the classical theory of brittle fracture, based on Griffiths criterion - a notion of critical energy release rate -, and a fracture toughness k, are numerous (think for instance the issue of crack initiation) and penalize its validity as a good model. Are all attempts at building a macroscopic theory of fracture doomed? The variety and complexity of micromechanical phenomena would suggest that this is indeed the case. We believe however that structural effects still preside over fracture and consequently propose to modify slightly Griffith theory without altering its fundamental components so that it becomes amenable to the widest range of situations. The examples presented here will demonstrate that a revisited energetic framework is a sound basis for a theory which can be used at the engineering level and which reconciles seemingly contradictory viewpoints. To cite this article: G. Francfort, J.-J. Marigo, C. R. Mecanique 330 (2002) 225-233.  2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS fatigue / elasticity / surface energy / crack / debonding / fracture / calculus of variations

Etude de l’influence des défauts de petite taille sur le comportement à rupture avec le modèle de Dugdale régularisé

Le but du travail est de montrer, dans le cadre de la mécanique de la rupture avec le modèle de Dugdale régularisé des forces cohésives, que les défauts de petite taille devant la longueur caractéristique du matériau ont pratiquement peu d’influence sur les capacités de résistance d’une structure. On traite pour cela deux exemples : le cas d’une plaque préfissurée, puis le cas d’une plaque contenant une cavité circulaire. Les calculs sont effectués avec la méthode des éléments finis.

Griffith Theory Revisited

Throughout the section, Ω denotes a bounded connected open domain of ℝ N , 1 ≤N ≤3, with smooth boundary ∂Ω the surface measure of which is finite and such that Ω is the interior of \(\bar \Omega \). As such, Ω represents the crack-free reference configuration of an elastic body.