Résumé
A particular class of mechanical systems concerns diffuse non smooth problems for which unilateral conditions may occur within the whole studied domain. For instance, when contact and friction occur as interactions between a large number of bodies, such as for granular media, or with tensegrity structures, when cable slackening may occur on the whole structure.When such large scale structures are studied, their numerical simulation may take advantage of using domain decomposition (DD) solvers.We do not consider here an outer loop for dealing with non linearities and non smoothness that lead to a series of linear problems, each of them being solved with a classical DD solver as a black box, but we focus on algorithms that allow us to tackle the non smoothness issue at the subdomain level, with a single iterative loop. Such approaches have already be designed for mechanical assemblings with a limited number of unilateral conditions, or for multicontact situations.