Formulation and approximation of quasistatic frictional contact

Cocu, Marius; Pratt, Elaine; Raous, Michel

doi:10.1016/0020-7225(95)00121-2

Cited by 100 publications

(80 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…To conclude we pass to the limit as n → +∞. The proof of inequality (58) is similar to the one of [8]. By the compact imbedding of H 1 2 (∂Ω) in L 2 (∂Ω), we have that (u n (t)) n∈N * converges strongly towards u(t) in [L 2 (Γ 3 )] 2 for almost all t. The same convergence property holds for (β n u n ) n∈N * , thus relation (59) follows.…”

Section: Lemma 34 There Exists a Uniquementioning

confidence: 90%

See 1 more Smart Citation

Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion

Cocu

Rocca

2000

ESAIM: M2AN

Self Cite

View full text Add to dashboard Cite

Abstract. We consider a two dimensional elastic body submitted to unilateral contact conditions, local friction and adhesion on a part of his boundary. After discretizing the variational formulation with respect to time we use a smoothing technique to approximate the friction term by an auxiliary problem. A shifting technique enables us to obtain the existence of incremental solutions with bounds independent of the regularization parameter. We finally obtain the existence of a quasistatic solution by passing to the limit with respect to time.Résumé. Nous considérons un corpsélastique bidimensionnel soumisà des conditions de contact unilatéral avec frottement et adhésion sur une partie de sa frontière. Après avoir discrétisé la formulation variationnelle par rapport au temps, nous régularisons le terme de frottement dans un problème auxiliaire. Une technique de translation nous permet d'obtenir l'existence de solutions incrémentales bornées indépendamment du paramètre de régularisation. Nous obtenons finalement l'existence d'une solution quasi-statique en passantà la limite par rapport au temps.Mathematics Subject Classification. 35K85, 49J40, 73T05.

show abstract

Section: Lemma 34 There Exists a Uniquementioning

confidence: 90%

“…Next by using an argument similar as in [8], we obtain the existence of (u n ) n∈N * , (ũ n ) n∈N * and an element…”

Section: Lemma 33 There Exist Two Subsequencesmentioning

confidence: 99%

Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion

Cocu

Rocca

2000

ESAIM: M2AN

Self Cite

View full text Add to dashboard Cite

show abstract

“…Some of these conditions are formulated in terms of the directional derivative of j which consists, to the best of our knowledge, a trait of novelty of this paper. The proof of the existence result for (1.1) and (1.2) is based on a time-discretization method, similar to that used in [1,5] in the study of quasistatic contact problems for elastic or viscoplastic materials. Given a time step, we construct a sequence of quasivariational inequalities for which we prove the existence of the solution using a result recently obtained in [11].…”

Section: )mentioning

confidence: 99%

“…The reason lies in the considerable difficulties that the process of frictional contact presents in the modeling and the analysis because of the complicated surface phenomena involved. The variational analysis of some quasistatic contact problems can be found for instance in [2,3,5,9] within linearized elasticity.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials

Motreanu

Sofonea

1999

Abstract and Applied Analysis

View full text Add to dashboard Cite

We consider a class of evolutionary variational inequalities arising in quasistatic frictional contact problems for linear elastic materials. We indicate sufficient conditions in order to have the existence, the uniqueness and the Lipschitz continuous dependence of the solution with respect to the data, respectively. The existence of the solution is obtained using a time-discretization method, compactness and lower semicontinuity arguments. In the study of the discrete problems we use a recent result obtained by the authors (2000). Further, we apply the abstract results in the study of a number of mechanical problems modeling the frictional contact between a deformable body and a foundation. The material is assumed to have linear elastic behavior and the processes are quasistatic. The first problem concerns a model with normal compliance and a version of Coulomb's law of dry friction, for which we prove the existence of a weak solution. We then consider a problem of bilateral contact with Tresca's friction law and a problem involving a simplified version of Coulomb's friction law. For these two problems we prove the existence, the uniqueness and the Lipschitz continuous dependence of the weak solution with respect to the data.

show abstract

“…Some examples of non unique solutions have been obtained for non analytical non smooth loading conditions on very simple systems in [22]. Uniqueness of continuum and finite element solutions have been proved for quasi-static frictional contact problems when a non local friction law is used and for small friction coefficient only [23,24]. The friction law that is used in this paper is the classical Coulomb's law.…”

Section: Introductionmentioning

confidence: 99%

A suitable computational strategy for the parametric analysis of problems with multiple contact

Boucard

Champaney

2003

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYThe aim of the present work is to develop an application of the LArge Time INcrement (LATIN) approach [1] for the parametric analysis of static problems with multiple contacts. The methodology adopted was originally introduced to solve viscoplastic and large-transformation problems [2,3]. Here, the applications concern elastic, quasi-static structural assemblies with local nonlinearities such as unilateral contact with friction. Our approach is based on a decomposition of the assembly into substructures and interfaces. The interfaces play the vital role of enabling the local nonlinearities, such as contact and friction, to be modeled easily and accurately. The problem on each substructure is solved by the finite element method and an iterative scheme based on the LATIN method is used for the global resolution. More specifically, the objective is to calculate a large number of design configurations. Each design configuration corresponds to a set of values of all the variable parameters (friction coefficients, prestress) which are introduced into the mechanical analysis. A full computation is needed for each set of parameters. Here we propose, as an alternative to carrying out these full computations, to use the capability of the LATIN method to re-utilize the solution to a given problem (for one set of parameters) in order to solve similar problems (for the other sets of parameters).

show abstract

Formulation and approximation of quasistatic frictional contact

Cited by 100 publications

References 9 publications

Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion

Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion

Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials

A suitable computational strategy for the parametric analysis of problems with multiple contact

Contact Info

Product

Resources

About