This chapter is dedicated to Professor Pierre Ladevèze on the occasion of his 60th birthday. As two former students of Pierre Ladevèze, the authors have both had the opportunity to work with domain decomposition methods in their research and teaching activities. Pierre initiated a mixed domain decomposition method within the framework of the LArge Time INcrement method. Such an approach is described herein, and its usefulness is exemplified for non-linear problems involving unilateral conditions, such as contact problems. Friction and damage can be taken into account, and an extension to a multilevel scheme is also described.