# University of Minnesota

Aerospace Engineering and Mechanics

**Spring 2000 Seminar Series**

*Numerical methods for an energetic formulation of brittle fracture*

*Abstract*

### In 1998, Gilles Francfort an Jean-Jacques Marigo have proposed a
variational formulation for quasi-static fracture of brittle materials. In this
setting, to each crack plus deformation state of a material submitted to a
given load, an energy made of 2 parts is associated. The first term is the bulk
energy computed on the uncracked part of the material while the second is
proportional to the length (or the surface in 3D) of the crack set. The
equilibrium configuration is then assumed to minimize this energy among all
crack sets and all associated deformation states. The numerical implementation
of this problem falls into the more general framework of free discontinuities
problems and the double dependence (geometrical for the crack set and
functional for the deformation field) requires the use of adequate tools taken
from the geometric measure theory and the theory of Gamma-convergence. In my
talk, I will briefly present the above mentioned model and the theoretical
tools involved in its study. Then, I will detail and compare two numerical
approaches and present some numerical experiments. Finally, I will present some
applications of these methods to different problems in structure mechanics.

### Friday, February 11, 2000

209 Akerman
Hall

2:30-3:30 p.m.

### Refreshments served after the seminar in
227 Akerman Hall.

Disability accomodations provided upon request.

Contact AEM Department 612-625-8000.