Reseach objectives and content The aim of this project is to develop advanced mathematical methods applicable to the theoretical and numerical study of unilateral problems involving composite finite bodies. We intend to propose new and efficient methods to model interface phenomena arising in composite bodies subjected to unilateral constraints like contact with friction and cleavaqe. Recent mathematical methods studied and developed by D. Goeleven (the applicant) and the team of P.D. Panagiotopoulos (the scientist in charge, of the proposal) will be applied so as to study and validate the proposed models. Algorithms for the numerical treatment of our problems will be developed and numerical examples will be examinated so as to check the, theoretically predicted stability and accuracy of the proposed methods. Training content (objective, benefit and expected impact) The whole project concerns a topic of growing maturity involvinq various new and efficient mathematical methods in the field of pure and applied nonlineat analysis and engineering sciences. The achievement of such project needs therefore a real and active cooperation between mathematicians and engineers. The host institution employing permanent engineers and numerous visiting outstanding mathematicians will provide a particularly suitable environment for the applicant. Numerous and fruitfull scientific cooperations with the researchers and the visiting researchers of the host institution will give to the applicant a solid training and scientific experience.