Unified model for Mullins effect and high cycle fatigue life prediction of rubber materials

Proceedings of the 8th European Conference on constitutive models for rubbers (ECCMR VIII), San Sebastian, Spain, 25-28 June 2013International audienceThe study describes the basic principles of a general damage model (GDMF) for Mullins effect and high cycle fatigue loadings of rubber materials and demonstrates its prediction possibilities for simulating the complete fatigue failure phenomenon. The present paper focuses on stiffness modelling of rubber materials for uniaxial and multiaxial static and fatigue loadings with a minimal number of material parameters in order to ensure robustness of the identification. The proposed hyperplastic model is expressed in terms of classical independent strain invariants. Mullins effect and high cycle fatigue loadings are both modelled according to a continuum damage mechanics approach

Éléments de géométrie pour la mécanique des milieux continus

Ce texte est le résultat d'un dialogue entre mathématiciens et mécaniciens. Il est destiné à faire le point sur le sujet des grandes déformations, d'un point de vue géométrique, en y maintenant un discours mathématique rigoureux tout en restant accessible et proche des préoccupations des mécaniciens

Non local damage model Boundary and evolving boundary effects

International audienceThe present contribution aims at providing a closer insight on boundary effects in non local damage modelling. From micromechanics, we show that on a boundary interaction stress components normal to the surface should vanish. These interaction stresses are at the origin of non locality and therefore the material response of points located on the boundary should be partially local. Then, we discuss a tentative modification of the classical non local damage model aimed at accounting for this effect due to existing boundaries and also boundaries that arise from crack propagation. One-dimensional computations show that the profiles of damage are quite different compared to those obtained with the original formulation. The region in which damage is equal to 1 is small. The modified model performs better at complete failure, with a consistent description of discontinuity of the displacement field after failure

Characterization of the symmetry class of an Elasticity tensor using polynomial covariants

We produce a minimal set of 70 generators for the covariant algebra of a fourth-order harmonic tensor, using an original generalized cross product on totally symmetric tensors. This allows us to formulate coordinate-free conditions using polynomial covariant tensors for identifying all the symmetry classes of the elasticity tensor and prove that these conditions are both necessary and sufficient. Besides, we produce a new minimal set of 297 generators for the invariant algebra of the Elasticity tensor, using these tensorial covariants

An assessment of the role of the third stress invariant in the Gurson approach for ductile fracture

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Courbe de convergence d’un tunnel pour un modèle phénoménologique d’endommagement

Une solution semi-analytique au calcul de la courbe de convergence d’un terrain est présentée. Les non-linéarités des matériaux rocheux sont modélisées en utilisant le formalisme de l’endommagement phénoménologique isotrope. Une validation de la solution par la méthode des matrices de transfert est proposée. Le tunnel du Bois de Peu. près de Besançon, sert d’application concrète aux calculs montrant la possibilité d’utiliser la mécanique de l’endommagement pour le dimensionnement en travaux souterrains

Analytical strain localization analysis of isotropic and anisotropic damage models for quasi-brittle materials

Strain and damage localization are usually precursors of rupture. We present a three-dimensional method dedicated to quasi-brittle materials based on the works of Bigoni & Hueckel, and Jirásek and coworkers, aiming at simplifying the analysis of the localization properties of continuous damage models of a general form, and possibly anisotropic. The method reformulates the localization problem as a two-variable polynomial maximization problem, a strategy commonly used in softening plasticity models, but not so much in Continuum Damage mechanics. The quasi-brittle hypothesis is exploited to render the problem solvable in a fully analytical way, and a post-analysis criterion for the validity of the analysis is also exhibited. In this work, the method is fully established from a theoretical viewpoint, and examples illustrating its use are provided. Multiaxial calculations are performed for four continuous damage models (two isotropic and two anisotropic ones). The method applies to induced anisotropy and constitutive models representing isotropic linear elasticity before damage growth, and remains accurate when models display immediate softening after the elastic limit (and thus to multiaxial tensile cases). The analytical method is, however, entirely general and allows for the calculation of (i) the orientation of a potential localization plane, (ii) the mode angle of the weak discontinuity, and (iii) the validity domain of such a simplified analysis