A thermodynamical approach to contact wear as application of moving discontinuities

International audienceThe propagation of a moving surface inside a body is analysed within the framework of thermomechanical couplings when the moving surface is associated with an irreversible change in mechanical properties. The moving surface is a surface of heat sources and of entropy production whose intensities are related to particular energy release rates defined in terms of Hamiltonian gradients. For example, we analyse the wear process. Wear phenomena due to contact and relative motion between two solids depend on the loading conditions and material mechanical properties. Friction between contacting bodies induces damage of materials, producing surface and subsurface cracks. Particles are detached from sound solids when some local criteria are satisfied at the boundary. As wear occurs, geometrical changes take place and contact conditions are modified, and the particle induces a specific layer with particular properties. Then the interface between the bodies is a complex medium made of detached particles, eventually a lubricant fluid, and damaged zones. We propose to describe the evolution of the interface using a framework developed earlier for inducing the general form of a wear law

Only thickness is essential in the Thick Level Set approach

Regularized damage formulations have become increasingly popular in the last decades for dealing with problems inMechanics suffering from spurious mesh sensitivity induced by strain softening [1]. In short, the idea underlying almost all such models is that of using some extended constitutive equations in which a length scale parameter brings to the macro level information about material microstructure. Classical regularized constitutive relationships are formulated via gradient or averaging operators. They provide globally smoothed solutions by enforcing a greater regularity either on strains or internal variables that are no longer defined at the quadrature point level but are established at a larger scale, i.e. the scale of the structural model. The same concepts are present into the so-called Thick Level Set (TLS) approach to quasi-brittle fracture [2], whereby progressive damage that takes place in a region of finite thickness is defined as an explicit function of the distance to the undamaged portion of the domain under consideration. Within this framework one possible way to follow the evolution of damage in the structure amounts to continuously tracking the position of the moving layer where the transition between the damaged material and the undamaged one occurs. In the original implementation of the model [2] this was achieved based on distance functions and level sets, which basically amounts to solve the eikonal equation. In the present contribution the eikonal-based approach to the TLS modeling is abandoned in favor of an implicit representation of the damage field and tools of convex analysis [3]. This allows to drop out the level sets from the formulation and to achieve a greater flexibility in the implementation of the model that is recast in the format of a non-local Generalized Standard Model in which the damage field is subject to convex constraints. Numerical results for representative test cases will be presented to demonstrate the capabilities of the proposed approach

Stability and Bifurcation in Nonlinear Mechanics

Analysis of stability and bifurcation is studied in nonlinear mechanics with mechanisms of dissipation: plasticity, damage, fracture. With introduction of a set of internal variables, this framework allows a systematic description of the material behavior via two potentials: the free energy and the potential of dissipation. For standard generalized materials, internal state evolution is governed by a variational inequality depending on the mechanism of dissipation. This inequality is obtained through energetic considerations in an unified description based upon energy and driving forces associated with internal variable evolution. This formulation provides criterion for existence and uniqueness of the system evolution. Examples are presented for plasticity, fracture and damaged materials

Modèles d'endommagement par level-set épaisse : solutions analytiques et simulations

Titre du résumé joint : Modélisation de l'endommagement par l'évolution d'une fonction de niveau le modèle TLS (Thick Level Set)National audienceEn endommagement brutal, la rupture se fait le long d'une frontière mobile accompagnée de discontinuités fortes du gradient du déplacement. On propose un modèle d'endommagement plus régulier fondé sur le mouvement d'une couche de largeur finie lc au sein de laquelle l'endommagement varie de façon continue. Cette approche permet dans un même cadre d'initier et de propager des défauts.See http://hal.archives-ouvertes.fr/docs/00/59/27/32/ANNEX/r_E3IGVTN6.pd

Application du contrôle optimal à l'identification d'un chargement thermique

La détermination du champ de température sur certaines pièces d'un moteur est obtenue par la résolution d'un problème inverse. Une alternative aux méthodes expérimentales coûteuses utilisées aujourd'hui est la méthode du contrôle optimal qui permet d'estimer le champ de température à partir de quantités mesurées sur pièce. Différents tests préfigurent des possibilités de prédiction et de fiabilité de la méthode