Seminars & Events

Mathematics and Computer Science Division Seminar
"Numerical Simulation of Quasi-Statis Brittle Fracture Using a Variational Model"

DATE: November 9, 2007
TIME: 1:00 pm
SPEAKER: Blaise Bourdin, Louisiana State University
LOCATION: Building 221 Conference Room A216, Argonne National Laboratory
HOST: Matt Knepley

Description:
Most widely accepted theories for modeling brittle fracture are based on Griffith's criterion and limited to the propagation of an isolated, pre-existing crack along a given path. The variational formulation, proposed by G. Francfort and J.-J. Marigo extends Griffith's theory into a global minimization principle, while preserving its essence, the concept of energy restitution in between surface and bulk terms. In its current state, it involves successive minimizations of a total energy with respect to any admissible displacement and crack field. The main advantage of this approach is to be capable of predicting the initiation of new cracks, computing their path, and accounting the interactions between several cracks, in two and three space dimensions. Of course, this has a price both theoretically and numerically. In particular, in order to achieve global minimization with respect to any crack set, one has to devise special numerical methods, typically based on the idea of approximation of functionals in the sense of the Gamma-convergence.

After a brief presentation of the variational model, I will describe its numerical implementation and highlight the challenges it poses. I will present various large scale numerical experiments. Time permitting, I will present some extensions of the models, and their requirements in terms of numerical implementation.

More Information:
Visitors from outside Argonne National Laboratory need gate clearance to enter the site. Please call the Mathematics and Computer Science Division at 630-252-7162.

Non-U.S. citizens need to allow 7 days for gate pass clearance approval.
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