Abstract
Abstract This paper is devoted to the analysis of the two- or three-dimensional elastic contact problem with Coulomb friction, quasi-static equilibrium, and small displacements. The classical approach is based on two minimum principles, or variational inequalities: the first for unilateral contact and the second for friction. In practical applications, this leads to an algorithm of alternately solving the two problems until convergence is achieved. A coupled approach using one principle or one inequality only is presented. This new approach, based on a model of material called implicit standard, allows for extension of the notion of a normality law to dissipative behavior with a nonassociated flow rule, such as surface friction. For numerical time integration of the laws, Moreau's implicit method is considered. Nondifferentiable potentials are regularized by means of the augmented Lagrangian technique. A discretized formulation using the finite element method and numerical applications are reported in a s...
Highlights
During the two last decades, many papers dealing with contact problems using the finite element method have been written
The success of the standard material approach follows from the possibility of associating variational functionals to deduce good properties for the boundary-value problems
In order to avoid this undesirable lack of normality and to extend the classical variational calculus to nonstandard materials, it is shown to be necessary to abandon the explicit form of the constitutive law
Summary
During the two last decades, many papers dealing with contact problems using the finite element method have been written. For unilateral contact with friction between elastic bodies, the new material law model leads to a single displacement variational principle for which the unilateral contact and the fricton law are coupled This variational approach is simpler than the classical one, which involves two variational principles, one for unilateral contact and the other for friction [7, 8, 12, 22]: When displacements are expressed with respect to traction, as in global GSM theory [18], the problem may be presented in inequality form. A similar algorithm using a projection step was presented by Giannakopoulos [32] and by Cumier and Alart [7] but starting from an approximation of the unilateral contact law by classical penalty techniques and of the friction law by a fictious elastoplastic-like law This is an extension of the approach known in elastoplasticity as the return mapping method, which is a particular case of Moreau's catching-up algorithm [I, 3, 4]. Other relevant features of contact problems, such as dual solutions by equilibrium and hybrid finite elements or accuracy problems due to geometrical modeling by finite elements, have been analyzed previously by De Saxce and Nguyen Dang Hung [35,36,37,38]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
