Claude Stolz

Mechanical transformations and discontinuities along a moving surface

Abstract Partial damage is considered in this paper. It is defined as a transformation of mechanical properties between two materials along a surface, in elasticity or anelasticity. The transformation is controlled by a generalized energy criterion of the Griffith type. The equilibrium state of the structure, the total dissipation with increasing loading and the associated rate boundary value problem are studied within the framework of generalized standard materials. A global formulation of the rate boundary value problem allows us to characterize the actual equilibrium state assumed to be known. Finally, the condition of stability and the possibility of bifurcation are given, as are applications to simple composite structures.

An optimal control approach to the analysis of inelastic structures under cyclic loading

Optimal control theory is used to study the asymptotic behaviour of elasto-viscoplastic structures under cyclic loading. With this approach, the asymptotic state is found as the solution of a minimization problem. General properties of this method are established. A simple thermomechanical problem is studied to illustrate and validate this approach. An interest of the proposed method lies in its capacity to handle other nonlinearities than plasticity. To illustrate this point, the approach is extended to the coupled viscoplasticity/frictionless contact problem. Some numerical results are given for an elasto-viscoplastic half-plane under cyclic frictionless indentation.

A new model of damage: a moving thick layer approach

A new formulation of a damage law is proposed based on a continuous transition between a sound material and a totally or partially broken material. The evolution of damage is then associated with a moving layer. This point of view permits the description of initiation and propagation of defects in an unified framework. The motion of the thick layer is defined in the frame of the moving surface Γo separating the sound material and the damaged material. When the damage parameters are continuous functions of the distance to Γo, they satisfy the conditions of transport. For particular geometries and loadings the evolution of the system is discussed. Comparison with description of damage with discontinuities and sharp interface is also presented.

Approche par contrôle optimal des structures élastoviscoplastiques sous chargement cyclique

Resume On utilise lapproche du controle optimal pour etudier le comportement asymptotique de structures elastoviscoplastiques sous chargement cyclique. Letat asymptotique est ainsi obtenu comme solution dun probleme de minimisation. On sinteresse a la mise en oeuvre pratique de cette methode en introduisant un probleme approche coherent avec une discretisation spatiale. Dans ce cadre, on montre que les seuls points stationnaires de la fonctionnelle a minimiser sont les minima globaux.

Thermodynamical Description of Running Discontinuities: Application to Friction and Wear

The friction and wear phenomena appear due to contact and relative motion between two solids. The evolution of contact conditions depends on loading conditions and mechanical behaviours. The wear phenomena are essentially characterized by a matter loss. Wear and friction are in interaction due to the fact that particles are detached from the solids. A complex medium appears as an interface having a strong effect on the friction condition. The purpose of this paper is to describe such phenomena taking account of different scales of modelization in order to derive some macroscopic laws. A thermodynamical approach is proposed and models of wear are analysed in this framework where the separation between the dissipation due to friction and that due to wear is made. Applications on different cases are presented.

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

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

SECTION 8.5 – A Thermodynamic Analysis of Wear

The interface is a complex medium made of detached particles, eventually a lubricant fluid, and damaged zones. In this chapter, the interface description is based on given macroscopic laws and differs from the one derived from microscopic considerations in Dragon-Louiset. The local approach allows making a distinction between mechanical quantities evaluated on a given geometry and for specific loading conditions and intrinsic ones associated with any moving wear surfaces. The approach to wear criteria in this chapter is based on the energy release rate like quantities, similar to Griffiths theory in fracture mechanics. All these quantifies some of them accessible to experiments, make it possible to better define wear criteria and wear rates. A system consisting of two sliding contacting solids and the contact interface zone, having some mechanical properties which are assumed to be known and described by usual laws of continuous media is considered. Such interface laws is understood in a macroscopic sense, as average or homogenized through the thickness of contact interface zone. The internal entropy production is positive and consists of different kinds of separately positive contributions: volumic thermal conduction, volumic intrinsic mechanical irreversibility, and surface irreversibility terms.

Approche variationnelle du comportement des milieux hétérogènes en thermoélasticité linéaire

Resume La demarche de Hashin et Shtrikman dencadrement des modules effectifs dun milieu elastique heterogene est appliquee, dans sa forme generalisee, au cas ou le milieu est thermoelastique lineaire. Cette demarche, fondee sur une approche energetique, permet lencadrement de lenergie libre globale du systeme, en sappuyant sur les principes de minimum de lenergie. Cette analyse est menee dans le cadre general dune description de la repartition des phases a laide de la notion de motif morphologique representatif.

Approche thermodynamique des phénomènes liés à l'usure de contact

On propose un cadre theorique detude des phenomenes dusure dus au contact entre deux solides. Lusure est caracterisee par la perte de matiere des solides en contact. Les particules detachees ainsi que les parties endommagees des deux solides forment une interface aux proprietes mecaniques complexes. Les zones frontieres des deux solides, en contact avec ce milieu, sont le siege dune dissipation associee a la perte de matiere des corps en contact. Un taux de restitution denergie associe a cette dissipation dusure est defini et sert a lelaboration dun critere. On examine le cas de lusure continue et on met en evidence des quantites globales caracteristiques du phenomene dusure.

Modeling Radiation Effects on the Fracture Process in Simplified Nuclear Glass

Experimentally, the evolution of several mechanic properties (hardness, density, Young’s modulus, fracture toughness) is observed in nuclear glasses under irradiation. In this work, classical molecular dynamics calculations are performed to better understand fracture mechanisms in simplified nuclear glasses at atomistic scale and to explain the radiation effects. Fractures are simulated in more disordered glasses, representative of irradiated samples, to reveal radiation effects. We observe a lower elastic limit and a greater plasticity in the irradiated glass that can explain its larger fracture toughness.