分野別セミナー

This talk focusses on the the variational approach to fracture,
devised by G.A. Francfort and J.-J. Marigo in 1998. In this approach,
the quasi-static evolution of the deformation and crack configuration
of a brittle solid is given by unilateral global minimization of a
total energy consisting in the sum of the body's elastic energy and a
crack surface energy proportional to its length (in 2d) or its area
(in 3d). This problems falls in the broader category of free
discontinuity problems. I will briefly present the model in the
context of Griffith's criterion, and give a few elements of analysis
before focusing on it snumerical implementation. I will present a
numerical approach based on elliptic regularization and illustrate it
with numerical experiments. I will then present some extensions and
applications to thermal fracture, peeling, drying, and dynamic
fracture.