Michel Raous

Formulation and approximation of quasistatic frictional contact

A quasistatic unilateral contact problem with a non-local friction law is considered We propose a new variational formulation of this problem consisting of two inequalities. By applying an implicit time discretization scheme, we obtain an incremental formulation which, if the friction coefficient is sufficiently small, has a unique solution for which appropriate estimations are obtained. This incremental solution enables us to construct a solution to the quasistatic problem by establishing the weak convergence of a subsequence of mappings interpolating the incremental solution. An algorithm is derived and a simple numerical example is presented.

Consistent time discretization for a dynamical frictional contact problem and complementarity techniques

Abstract.The dynamical problem of a viscoelastic body involving unilateral contact and Coulomb friction is set so as to take into account accurately eventual discontinuities of the relative velocit...

Creep crack initiation and creep crack growth assessments in welded structures

Abstract In this study, creep crack initiation and creep crack growth in welded structure are analysed. An interaction phenomenon between base metal and weld metal in a cross weld plate is highlighted with a finite element model. A simplified method based on the reference stress approach is proposed to evaluate C * in welded structures. This simplified method is applied for creep crack initiation and creep crack growth assessments in the case of a double edge notched tension cross-welded plate. Correlations between crack initiation time and C * on the one hand, and between creep crack growth rate and C * on the other hand are used. Creep crack initiation time estimation for the full size welded plate is very conservative when crack initiation properties of CT specimen are used. Concerning creep crack growth evaluation, simplified estimation is in good agreement with experimental results when CT specimen crack propagation properties are used.

UNILATERAL CONTACT, FRICTION AND ADHESION: 3D CRACKS IN COMPOSITE MATERIALS

The model coupling adhesion, unilateral contact and friction, developed by M. Raous, L. Cangemi and M. Cocou, is extended here for studying propagating cracks in fiber-reinforced composites. The brittle fracture of the bulk materials (fiber and matrix) is described by a time-independent version of the model. In this case, jumps in the evolution of the solution may occur and a dynamic formulation has to be used. This is performed by adapting a dynamic formulation due to J.J. Moreau and M. Jean to this problem. Numerical simulations of 3D fracture of composite materials are then presented.

Multigrid Methods for Unilateral Contact Problems with Friction

In this paper, multigrid methods are tested on unilateral problems with friction. An optimal strategy is presented and efficiency of the solver is discussed on several examples.

Numerical characterization and computation of dynamic instabilities for frictional contact problems

This chapter focuses on the numerical aspects of the characterization of friction-induced instabilities and their dynamic computation for linear and nonlinear problems. We begin by presenting briefly basic formulations and several computational methods for solving unilateral frictional contact problems, in quasi-statics and dynamics, and in elasticity and hyper-elasticity. The above specific dynamic formulations will be used to compute the flutter solutions presented in the last sections. Numerical schemes are then given for computing the various sufficient or necessary conditions for instability established together with Professor J.A.C. Martins Finally, the stability analysis and the computation of flutter solutions are carried out for two examples: the sliding of a Polyurethane block on a plane and the squeal of a rubber waist seal sliding on a car window.

Analysis of an Incremental Formulation for Frictional Contact Problems

This work concerns a quasistatic Signorini’s problem with a nonlocal Coulomb’s friction law for a linear elastic body. When unilateral contact and friction are considered, both displacement (normal contact) and velocity (friction) are involved. The static (displacement) formulation cannot describe evolutive situations, however introducing the unilateral condition uN≤0 into the dynamic formulation is not so simple as uN, in some situations, may be either positive or negative.

Constructive aspects of functional analysis for the treatment of frictional contact

This paper is a survey of our results concerning frictional unilateral contact problems. Mathematical and numerical results obtained over the past few years for both static and quasistatic problems are summarized. Undergoing developments concerning viscoelastic quasistatic problems are outlined.

Friction and Adhesion

The studies carried out on adhesion by the group “Modeling in Contact Mechanics” at the LMA are reviewed in this paper and recent applications are presented. Based on the introduction of the adhesion intensity variable developed by M. Fremond, different forms of a model coupling adhesion to unilateral contact and friction have been developed. The formulations are given either under the form of implicit variational inequalities or the one of complementarity problems. Both quasi-static and dynamic formulations are considered.

Détermination du module d'Young opérationnel d'un corps viscoélastique à partir de sa courbe de relaxation

Dans un corps viscoelastique, la contrainte et la deformation sont liees par une relation differentielle. Dans un certain domaine, nous pourrons considerer cette relation comme lineaire, et l’ecrire, alors dans l’espace de Laplace sous la forme: