Numerical modelling and simulation of frictional contact using a generalised coulomb law

Abstract

A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi-static Finite Element Method. Analogous to classical work hardening theory in elasto-plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep-drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.

Méthode de Newton généralisée en mécanique du contact

“…Cet article rassemble un certain nombre de résultats obtenus au cours des dernières années ; chacun d'entre eux ne constitue qu'une réponse partielle, mais pris dans leur ensemble, ils fournissent les raisons de la confiance que nous avons dans cette approche, entretenue par ailleurs par son efficacité sur des problèmes industriels [ 6,17,18,24]. Des techniques multigrilles ou parallèles tout à fait spécifiques sont en cours de développement afin de réduire le temps calcul des algorithmes [7,8].…”

Algorithms and Strategies for Treatment of Large Deformation Frictional Contact in the Numerical Simulation of Deep Drawing Process

“…The results presented disclose the versatility of the mixed formulation in dealing with global evolutions of the friction coefficient. However, due to the difficulties related with measuring the local variations of the friction coefficient, it is very difficult to correlate effectively the law described with experimental results [121]. The mixed formulation of contact with friction is also applicable to describe anisotropic behaviour of Coulomb's friction coefficient.…”

“…In fact, the Coulomb's friction law can be generalised to consider the friction cone evolution according with one or more internal variables. Neglecting the anisotropic component of friction, it is only necessary to change the friction law and the complementary condition to [121]:…”

Development of normal pressure and frictional traction along the walls of a steep conical hopper during filling

“…Modelling such a mechanical interaction can be quite complex, and is still a great challenge [32,33,34,35] . In the current study, since the focus is to find an alternative approach to explore the loads as developed along the walls of a hopper during filling, the interaction between the contacting surfaces of the hopper and the stored particulate solids was modelled with a very simplified constitutive model of Coulomb friction [34,35,36]. A constant friction coefficient μ was assumed and implemented in the model.…”