| back to Research Teams | Mathematical and numerical methods in Mechanics Members (Ph. D.) Barbarosie, Cristian Students Lopes, Nuno David de Jesus External Collaborators Mascarenhas, Maria Luísa Keywords Calculus of Variations; Shape and topology optimization; Differential inclusions in Mechanics; Harmonic maps; Dislocations, Brittle and ductile fracture Objectives - Minimization, in the space of special functions of bounded variation, of energy functionals including bulk and surface energy terms, subject to boundary conditions. - Study of asymptotic developments of solutions of elliptic problems relative to the volume of an infinitesimal inclusion/hole, as related to the topological shape derivative and Saint-Venant’s principle. - Study of properties of cost functionals in free material optimization, with special emphasis on lower semicontinuity in H-topology. - Qualitative behaviour of ppmc isometric immersions. - Infinitesimal deformation of harmonic maps. - Study of stability of quasi-static paths for 1-D deformable media. - Study of dynamics with friction, including Painlevé’s examples. - Study of non-convex differential inclusions, involving orders. - Study of Euler equations with non-homogeneous boundary conditions. - Discretization of Navier-Stokes equations - Dislocation models (geometry, dynamics & homogenization) - Fracture models (numerical simulation of brittle fracture by level-set and topological methods & ductile elasto-plastic fracture
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