Objectif This research project deals with nonlinear evolution problems that arise in the study of the inelastic behaviour of solids, in particular in plasticity and fracture. The project will focus on selected problems, grouped into three main topics, namely:1. Plasticity with hardening and softening, 2. Quasistatic crack growth, 3. Dynamic fracture mechanics.The analysis of the models of these mechanical problems leads to deep mathematical questions originated by two common features: the energies are not convex and the solutions exhibit discontinuities both with respect to space and time. In addition, plasticity problems often lead to concentration of the strains, whose mathematical description requires singular measures. Most of these problems have a variational structure and are governed by partial differential equations. Therefore, the construction of consistent models and their analysis need advanced mathematical tools from the calculus of variations, from measure theory and geometric measure theory, and also from the theory of nonlinear elliptic and parabolic partial differential equations. The models of dynamic crack growth considered in the project also need results from the theory of linear hyperbolic equations.Our goal is to develop new mathematical tools in these areas for the study of the selected problems. Quasistatic evolution problems in plasticity with hardening and softening will be studied through a vanishing viscosity approach, that has been successfully used by the P.I. in the study of the Cam-Clay model in soil mechanics. Quasistatic models of crack growth will be developed under different assumptions on the elastic response of the material and on the mechanisms of crack formation. For the problem of crack growth in the dynamic regime our aim is to develop a model that predicts the crack path as well as the time evolution of the crack along its path, taking into account all inertial effects. Champ scientifique natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Appel à propositions ERC-2011-ADG_20110209 Voir d’autres projets de cet appel Régime de financement ERC-AG - ERC Advanced Grant Institution d’accueil SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE Contribution de l’UE € 968 500,00 Adresse VIA BONOMEA 265 34136 Trieste Italie Voir sur la carte Région Nord-Est Friuli-Venezia Giulia Trieste Type d’activité Higher or Secondary Education Establishments Chercheur principal Gianni Dal Maso (Prof.) Contact administratif Gabriele Rizzetto (Mr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE Italie Contribution de l’UE € 968 500,00 Adresse VIA BONOMEA 265 34136 Trieste Voir sur la carte Région Nord-Est Friuli-Venezia Giulia Trieste Type d’activité Higher or Secondary Education Establishments Chercheur principal Gianni Dal Maso (Prof.) Contact administratif Gabriele Rizzetto (Mr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée