Marco Artina's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT

Marco Artina
(Technische Universität München)

Title: A robust and ecient anisotropic mesh adaptation strategy to 
numerically simulate quasi-static crack propagation in brittle materials

Abstract: The numerical simulation of quasi-static fracturing of brittle 
material, where no pre-de
ned crack path is imposed, is a challenging 
problem. In particular,
we deal with the Francfort-Marigo model which requires the minimization 
of the well-known nonconvex and nonsmooth Mumford-Shah functional. To deal
with a smoother functional which eases the minimization process of the 
energy, we consider the -approximation of the Mumford-Shah functional 
via the
Ambrosio-Tortorelli functional. Moreover, from a modeling viewpoint, we 
induce the quasi-static crack evolution via an applied displacement 
slowly changing in time.
It is a well-established fact that the numerical simulation is often 
biased by an improper numerical discretization, with potential 
non-physical results. In particular, a non-optimal or a 
xed 
computational mesh can a
ect the fracture evolution, driving it along 
non-realistic directions, like the edges of the triangulation. This 
issue can be successfully tackled by resorting to anisotropic adapted 
meshes, which have been successfully employed to model phenomena 
exhibiting strongly directional features.
To drive mesh adaptation, we elaborated an a-posteriori anisotropic 
error estimator for the proper discretization of the energy functional. 
Through anisotropic meshes we are able to locate, size and orient the 
mesh elements in order to follow the intrinsic directionalities of the 
solution at hand. Thanks to this grid adaptation process, we obtained 
solutions reliable from a physical viewpoint and with a relatively small 
computational cost.
In this talk, we introduce the Francfort-Marigo model and its 
-approximation in case of plane and antiplane displacements. Then, we 
focus on the anisotropic mesh adaptation strategy. We 
nally assess the 
reliability, robustness, and efficiency of the proposed approach on 
some benchmark tests.

Venue: SISSA, room 005 (ground floor), Friday 20 March at 11:00