A mixed formulation for frictional contact problems prone to Newton like solution methods
Computer Methods in Applied Mechanics and Engineering
Selecting contact particles in dynamics granular mechanics systems
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
The 3ß hyperelastic model applied to the modeling of 3D impact problems
Finite Elements in Analysis and Design
A reliable algorithm to solve 3D frictional multi-contact problems: Application to granular media
Journal of Computational and Applied Mathematics
A posteriori error analysis of a domain decomposition algorithm for unilateral contact problem
Computers and Structures
A hybrid iterative solver for robustly capturing coulomb friction in hair dynamics
Proceedings of the 2011 SIGGRAPH Asia Conference
Inverse dynamic hair modeling with frictional contact
ACM Transactions on Graphics (TOG)
An alternative formulation for quasi-static frictional and cohesive contact problems
Computational Mechanics
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Nowadays, the concept of convex potential of dissipation is a powerful tool customarily used to model the constitutive dissipative laws. Unfortunately, it fails when applied to Coulomb's dry friction contact, which is shown in this paper by checking the cyclic monotony condition. Next, a new approach, the bipotential method, is presented and successfully applied to the contact law. This enables us to write it in a compact form and to uncover an implicit normality rule structure. The advantages of the new approach are numerous, among which is emphasized a pretty extension of the calculus of variation. Two minimum principles of the so-called bifunctional are presented for contact problems. Next, the bipotential method can be qualified as constitutive in the sense that it suggests improved numerical algorithms. In particular, it is proved that the complete contact law can be rewritten as a projection equation onto Coulomb's cone. Numerical examples show the feasibility of the algorithm and the computer time reduction with respect to other previous numerical approaches.