The project focuses on a new limit analysis method, called Discontinuous Velocity Domain Splitting (DVDS) method. To solve the nonlinear PDE problem associated to ductile rupture (failure), DVDS considers a special class of velocity fields: the body is splinted into sub-domains animated by rigid motions. The collapse flow velocity field results in localized deformations only, located at the boundary of the sub-domains. The associated numerical technique is mesh free, it is based on a level set description of the partition and on genetic minimization algorithms.
For the scalar flow of a von-Mises material, DVDS is exact in solving the limit load problem. DVDS formulation reduces to the famous geometry problem of Cheeger, related to the eigenvalues of the Laplacian operator. One of the challenges of the present project is to know if these results are still valid in the vectorial case.
Two applications will be considered: dense avalanches onset of shallow natural structures and homogenization techniques for porous crystals. Due to the presence of the topography in the first case and the presence of the pores in the second one the material is strongly heterogeneous in both cases. Since DVDS is a mesh free technique, the resulting computational effort will be much less in comparison with other finite elements methods.
The project will take profit from high level scientific activities of IMAR and the computing laboratory recently implemented there.