Patrice Coorevits

Mixed finite element methods for unilateral problems: convergence analysis and numerical studies

In this paper, we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics. The discretized unilateral conditions at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. A priori error estimates are established and several numerical studies corresponding to the different choices of the discretized unilateral conditions are achieved.

An automatic procedure with a control of accuracy for finite element analysis in 2D elasticity

Abstract This paper gives a procedure for an automation of the entire finite element analysis for 2D or axisymmetric elastic structures with a control of accuracy. The user describes the problem and the level of desired accuracy. The procedure then provides an approximate solution for a minimal computation cost. This procedure uses an error measure based on the constitutive relation [1–5] and an efficient adaptive technique [6] which automatically take account of the regions of stress concentration. Examples are presented for discretizations using 3- or 6-node triangular elements.

A posteriori error estimation for unilateral contact with matching and non-matching meshes

In this paper, we consider the unilateral contact problem between elastic bodies. We propose an error estimator based on the concept of error in the constitutive relation in order to evaluate the finite element approximation involving matching and non-matching meshes on the contact zone. The determination of the a posteriori error estimate is linked to the building of kinematically-admissible stress fields and statically-admissible stress fields. We then propose a finite element method for approximating the unilateral contact problem taking into account matching and non-matching meshes on the contact zone; then, we describe the construction of admissible fields. Lastly, we present optimized computations by using both the error estimates and a convenient mesh adaptivity procedure. ” 2000 Elsevier Science S.A. All rights reserved.

A Posteriori Error Control of Finite Element Approximations for Coulomb's Frictional Contact

This paper is concerned with the frictional unilateral contact problem governed by Coulombs law. We define an a posteriori error estimator based on the concept of error in the constitutive relation to quantify the accuracy of a finite element approximation of the problem. We propose and study different mixed finite element approaches and discuss their properties in order to compute the estimator. The information given by the error estimates is then coupled with a mesh adaptivity technique which provides the user with the desired quality and minimizes the computation costs. The numerical implementation of the error estimator as well as optimized computations are performed.

A reliable algorithm to solve 3D frictional multi-contact problems: Application to granular media

We present in this paper an improved non-smooth Discrete Element Method (DEM) in 3D based on the Non-Smooth Contact Dynamics (NSCD) method. We consider a three-dimensional collection of rigid particles (spheres) during the motion of which contacts can occur or break. The dry friction is modeled by Coulombs law which is typically non-associated. The non-associativity of the constitutive law poses numerical challenges. By adopting the use of the bi-potential concept in the framework of the NSCD DEM, a faster and more robust time stepping algorithm with only one predictor-corrector step where the contact and the friction are coupled can be devised. This contrasts with the classical method where contact and friction are treated separately leading to a time stepping algorithm that involves two predictor-corrector steps. The algorithm has been introduced in a 3D version of the NSCD DEM software MULTICOR. Numerical applications will show the robustness of the algorithm and the possibilities of the MULTICOR software for solving three-dimensional problems.

Analyses éléments finis adaptatives pour les structures tridimensionnelles en élasticité

ABSTRACT The design of three-dimensional structures requires finite element computations, whose cost in human and computational time becomes prohibitive when a reasonable criterion of quality is imposed. Methods of control of the discretization errors and optimization of the parameters of the analysis enable the application of finite element analysis; yet, the main difficulty in 3D is the adaptivity of the meshes. The purpose of this paper is to present and compare several methods in order to address this difficulty.

Sur l'adaptativité des maillages à base de quadrilatères

ABSTRACT This paper gives a procedure of mesh adaptivity with quadrilateral elements. This procedure uses an error measure based on the constitutive relation, an efficient adaptive technique which automatically takes account of the singularities and the regions of stress concentration and a mesh generator of quadrilateral elements. We propose as application for 2D elastic structures the extension of automation of the finite element analysis which has been developed for triangular elements to the quadrilateral elements. The user describes the problem and the level of desired accuracy. The procedure then provides an approximate solution for a minimal computation cost with the respect of the desired accuracy. Examples are presented for discretizations using 4- or 8-node quadrilateral elements.

Modeling the discharge of a powder fire extinguisher by mixed discrete element method and computational fluid dynamics

A model that combines the discrete element method (DEM) and computational fluid dynamics (CFD) was developed for investigating the discharge of a powder fire extinguisher. The mathematical model is based on the equations of k-ε turbulent models coupled with the equations of particle motion. The discrete element method is used for obtaining the contact forces and the movement of individual particles. The contact force is calculated from the concept of friction slider and the flow field of gas is predicted by the Navier-Stokes equation. This DEM-CFD model provides the information needed to evaluate fire extinguisher performance.

Contrôle et adaptation des calculs éléments finis pour les problèmes de contact unilatéral

ABSTRACT In this paper, we present an error estimator for the contact problem of an elastic body on a rigid foundation in elasticity or Signorinis problem. The estimator is based on the concept of error in the constitutive relation and on techniques of admissible fields building. It is carrying into effect with a particular technique in order to take into account the contact. The convergence rate of this estimator is studied. By using procedures of mesh adaptivity previously developed, we show an example of optimized computations for discretizations with 3-nodes triangles.

Controlled cost of adaptive mesh refinement in practical 3D finite element analysis

In this paper, attention is restricted to mesh adaptivity. Traditionally, the most common mesh adaptive strategies for linear problems are used to reach a prescribed accuracy. This goal is best met with an h-adaptive scheme in combination with an error estimator. In an industrial context, the aim of the mechanical simulations in engineering design is not only to obtain greatest quality but more often a compromise between the desired quality and the computation cost (CPU time, storage, software, competence, human cost, computer used). In this paper we propose the use of alternative mesh refinement with an h-adaptive procedure for 3D elastic problems. The alternative mesh refinement criteria allow to obtain the maximum of accuracy for a prescribed cost. These adaptive strategies are based on a technique of error in constitutive relation (the process could be used with other error estimators) and an efficient adaptive technique which automatically takes into account the steep gradient areas. This work proposes a 3D method of adaptivity with the latest version of the INRIA automatic mesh generator GAMHIC3D.