Stabilised/Nitsche’s method for Contact Problems

Por Juha Videman (CAMGSD, Instituto Superior Técnico).

Abstract: Stabilization of mixed finite element methods for saddle point problems is a well-established technique that allows one to use finite element spaces that do not satisfy the Babuska-Brezzi condition. They were introduced and analysed in 80’s by Hughes, Franca, Brezzi, Pitkäranta and others. The analysis has, however, suffered from the fact that full regularity of the exact solution needs to be assumed.

Topological Sensitivity Analysis in Damage and Fracture Mechanics

Por Marcel Xavier (LNCC, Petropolis, Brasil).

Abstract: The topological derivative is a scalar field that measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation, such as the insertion of holes, inclusions, source-terms or even cracks. In this work, the concept of topological derivative is applied in the context of damage and fracture mechanics. In particular, the nucleation and propagation damaging process are studied.

On the area functional and related Plateau type problems

Por Riccardo Scala (University of Rome 1, “La Sapienza”).

Abstract: We introduce the notion of area of the graph of a smooth function and the definition of the corresponding relaxed functional. We discuss some issues related to determine the domain and the exact value of it on singular maps. Finally we show how this question is related to Plateau-type problems with mixed boundary conditions and how to solve it in some specific cases.