Material stability analysis based on the local and global elasto-plastic tangent operators

International audienceThe present paper investigates bifurcation in geomaterials with the help of the second-order work criterion. The approach applies mainly to non associated materials such as soils. The analysis usually performed at the material point level is extended to quasi-static boundary value problems, by considering the finite element stiffness matrix. The first part of the paper reminds some results obtained at the material point level. The bifurcation domain is presented in the 3D principal stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. In the second part, the analysis is extended to boundary value problems in quasi-static conditions. Non-linear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode even for non homogeneous boundary value problems

Divergence and flutter instabilities of some constrained two-degree-of-freedom systems

International audienceIt is now well ascertained that a variety of instability modes can appear before the conventional plastic limit condition is met. In this paper, both flutter and divergence instability modes are investigated. First, the mechanical meaning of these instability modes is reviewed, and the criterion for detecting their occurrence is established. Based on an illustration example, the competition between the occurrences of each of these instability modes is analyzed, showing that the prevalence of a given mode is strongly related to both the loading conditions and the stiffness properties of the material system in hand

Stability of non-conservative elastic structures under additional kinematics constraints

International audienceIn this paper, the specific effect of additional constraints on the stability of undamped non-conservative elastic systems is studied. The stability of constrained elastic system is compared to the stability of the unconstrained system, through the incorporation of Lagrange multipliers. It is theoretically shown that the second-order work criterion, dealing with the symmetric part of the stiffness matrix corresponds to an optimization criterion with respect to the kinematics constraints. More specifically, the vanishing of the second-order work criterion corresponds to the critical kinematics constraint, which can be interpreted as an instability direction when the material stability analysis is considered (typically in the field of soil mechanics). The approach is illustrated for a two-degrees-of-freedom generalised Ziegler's column subjected to different constraints. We show that a particular kinematics constraint can stabilize or destabilize a non-conservative system. However, for all kinematics constraints, there necessarily exists a constraint which destabilizes the non-conservative system. The constraint associated to the lowest critical load is associated with the second-order criterion. Excluding flutter instabilities, the second-order work criterion is not only a lower bound of the stability boundary of the free system, but also the boundary of the stability domain, for all mixed perturbations based on proportional kinematics conditions

On the stability of nonconservative elastic systems under mixed perturbations

International audienceThis paper shows that the loading mode strongly influences the stability of discrete non-conservative elastic systems. The stability of the constrained system is compared to the stability of the unconstrained system, through the incorporation of Lagrange multipliers. Initially, the approach is illustrated for a two-degrees-of-freedom generalized Ziegler's column. Then, it is applied to a two-degrees-of-freedom model representing a soil constrained with isochoric loading. The isochoric instability load is not necessarily greater than the instability load of the free problem. Excluding flutter instabilities, it is shown that the second-order work criterion is not only a lower bound of the stability boundary of the free system, but also the boundary of the stability domain, in presence of mixed perturbations based on proportional kinematic conditions.Cet article étudie l'influence du mode de chargement sur la stabilité de systèmes élastiques discrets non conservatifs. La stabilité du système contraint est comparée à celle du système libre, par l'introduction de multiplicateurs de Lagrange. L'approche est illustrée avec le pendule généralisé de Ziegler. Elle est ensuite appliquée à un modèle à deux degrés de liberté représentant un sol contraint par un chargement isochore. On montre que le chargement isochore affecte sensiblement la frontière de stabilité pour le problème conservatif et pour le problème non conservatif. En dehors des instabilités par flottement, le critère de travail du second-ordre constitue une borne inférieure de la frontière de stabilité du système libre ainsi que la frontière du domaine de stabilité du système sous chargements mixtes proportionnels en déplacement

Approche multi-échelle de la rupture

Dans de nombreuses applications du génie civil, la détection précoce d'un état de rupture constitue un enjeu fondamental. Dans le contexte de la géomécanique, une classe fondamentale de rupture pour un système, contrôlé par des paramètres bien définis, correspond à la création d'énergie cinétique sans évolution des paramètres de contrôle. Il est alors montré que de telles bifurcations peuvent être détectées par l'annulation du travail du second ordre, à l'échelle macroscopique, défini à partir du champ de variables contraintes-déformations tensorielles. En outre, tenant compte de la nature souvent discrète des géomatériaux, on établit que le travail du second ordre macroscopique, évalué à l'échelle d'un assemblage granulaire, correspond à la somme de tous les travaux du second-ordre microscopiques, évalués au droit de chaque contact de l'assemblage à partir des grandeurs discrètes. Cette équivalence micro-macro fondamentale donne lieu à une interprétation micro-structurelle de l'annulation du travail du second ordre au sein d'un assemblage granulaire

Constitutive models for predicting liquefaction of soils

Liquefaction is an example of a diffuse mode of failure. It occurs in loose sands when the effective mean pressure decreases to zero. This phenomenon has been studied extensively both experimentally and theoretically. Three constitutive laws, based on different assumptions, capable of predicting liquefaction are presented in the paper. These are Pastor-Zienkiewicz generalized plasticity model and Darve’s incrementally non-linear and octo-linear models. Results of numerical simulations of element tests are presented in the paper

A simple non-linear model for internal friction in modified concrete

International audienceIn this paper we consider a two-degrees-of-freedom, non-linear model aiming to describe internal friction phenomena which have been observed in some modified concrete specimens undergoing slow dynamic compression loads and having various amplitudes but never inducing large strains. The motivation for the theoretical effort presented here arose because of the experimental evidence in which dissipation loops for concrete-type materials are shown to have peculiar characteristics. Indeed, as (linear or nonlinear) viscoelastic models do not seem suitable to describe neither qualitatively nor quantitatively the measured dissipation loops, we propose to introduce a micro-mechanism of Coulombian internal dissipation associated to the relative motion of the lips of the micro-cracks present in the material. We finally present numerical simulations showing that the proposed model is suitable to describe some of the available experimental evidences. These numerical simulations motivate further developments of the considered model and supply a tool for the design of subsequent experimental campaigns

Modélisation des glissements de terrain avec une loi de comportement à transition solide/fluide

Modéliser les glissements de terrain implique la prise en compte de la complexité de ces phénomènes. En effet au cours de ceux-ci on peut distinguer une phase de rupture (solide) et une phase d'écoulement visqueux (fluide). Les méthodes numériques classiques étant difficilement capables de décrire à grande échelle ces deux types de comportement, nous avons choisi de travailler avec une méthode récente la Méthode des Éléments Finis avec des Points d'Intégration Lagrangiens (MEFPIL). Nous présenterons les premiers résultats obtenus avec la MEFPIL en comportement visco-élasto-plastique