The bi-potential method applied to the modeling of dynamic problems with friction

Abstract

The bi-potential method has been successfully applied to the modeling of frictional contact problems in static cases. This paper presents an extension of this method for dynamic analysis of impact problems with deformable bodies. A first order algorithm is applied to the numerical integration of the time-discretized equation of motion. Using the Object-Oriented Programming (OOP) techniques in Cþþ and OpenGL graphical support, a finite element code including pre/postprocessor FER/Impact is developed. The numerical results show that, at the present stage of development, this approach is robust and efficient in terms of numerical stability and precision compared with the penalty method.

A comparative study between two smoothing strategies for the simulation of contact with large sliding

“…La grande sensibilité de ce type de simulations numériques impose notamment un respect très précis des conditions de non pénétrabilité. La méthode de pénalité n'est donc pas utilisable dans notre cas et la méthode du bi-potentiel lui est préférée [10].…”

“…Il existe plusieurs méthodes permettant de résoudre ces problèmes parmi lesquelles : les éléments de type mortar [11,21,26], les méthodes de lissage de la surface de contact par ajout d'une entité géométrique (type B-spline ou NURBS) [8,16,15,22,38], ainsi que les analyses de type iso-géométriques [13,36,19]. Les travaux présentés dans cet article portent sur les deux derniers types de méthodes qui sont utilisées en combinaison avec un algorithme de traitement du contact avec la méthode du bi-potentiel [10]. Une étude comparative des avantages et inconvénients de chaque méthode en termes de précision géométrique et de stabilité de la solution du problème de contact associé.…”

“…Because very sensitive numerical phenomena may arise from this type of interactions such as modal interaction [32,18,6] or rubbing [23], contact must be managed very precisely and no penetration is acceptable. Consequently the penalty method is not eligible for our study and an augmented Lagrangian formulation combined with the bi-potential method proposed in [10] is used. In this formulation, the frictional contact problem is treated in a reduced system by means of a predictor corrector solution algorithm.…”

The Yeoh model applied to the modeling of large deformation contact/impact problems

“…A first order time scheme has also been proposed by Jean [6] for time stepping in granular mechanics. Recently, Feng et al [7,8] have applied this scheme for the modeling of impact problems between elastic bodies.…”

Identification of the dissipated energy by friction in dynamic multibody systems

“…The first order algorithm has also been proposed by Jean [7] for time stepping in rigid-body dynamic contact problems. Recently, Feng et al [6] have applied a Corresponding author: feng@iup.univ-evry.fr this algorithm for the modeling of impact problems between elastic bodies. The aim of the present paper is to apply the so-called Bi-First algorithm for contact modeling in dynamic cases between elastic and hyperelastic materials.…”