"The present project intends to introduce new uses of the level set representation of surfaces in order to develop simulation methods able to solve problem currently unsatisfactorily addressed. Three main applications are targeted: localisation phenomena and very complex cracking patterns, precise determination of stresses around contact zones and, finally, introduction in reasonably coarse meshes of the mechanical influence of geometrically small but vitally important reinforcement for the structure safety (weld points, cables, fillets, …). We plan to address them with a unified technology, parts of which are already being incorporated in codes worldwide because of the contribution of the PI and colleagues in the past ten years.The PI is a specialist in the field of computational mechanics and has been the founder and among the major promoters of the eXtended Finite Element Method (X-FEM), now widely used for crack growth and material interfaces modelling. With the X-FEM, internal or external mechanical boundaries do not need to be explicitly meshed and may conveniently be stored as level sets.The project proposes new algorithm based an original and extended use of the level set concept in conjunction with the X-FEM :*Thick Level Set (TLS): We consider that the mechanical variable responsible for the localization of deformation in a softening behaviour (say damage for instance) is not local but tied to the movement of a degradation front located by a level set.*Inequality Level Set (ILS): We rephrase variational inequality formulation (such as contact) as shape optimization. The shape of the active contact zone is sought and represented by a level set. For any given level set location, a variational equality is solved and a sensitivity analysis is performed to update the level set location.*Subgrid Level Set (SLS): The structural features (cables, fillets, …) are represented on a subgrid different from the mesh used to perform the computation."