University of Minnesota
Aerospace Engineering and Mechanics
Spring 2000 Seminar Series



Numerical methods for an energetic formulation of brittle fracture


Professor Blaise Bourdin

Department of Applied Mechanics and Mechanical Engineering

California Institute of Technology


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.