# Seminar.

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# Section 1. Seminar.

## Seminars at the Faculty of Informatics

### On the active control of crack growth in elastic media

The Faculty of Informatics is pleased to announce a seminar given by Patrick Hild

DATE: Thursday, October 29th, 2009
PLACE: USI Università della Svizzera italiana, room SI-15, Informatics building (Via G. Buffi 13)
TIME: 14.30

ABSTRACT:
Let S be a 2-D elastic structure submitted to a fixed boundary load f and containing a crack. In the framework of the linear fracture theory, a common tool used to describe the smooth evolution of the crack is the so-called energy release rate defined as the variation of the mechanical energy with respect to the crack dimension. Precisely, the well-known Griffith's criterion postulates the evolution of the crack if this rate - positive measure of the singularity which depends quadratically on the displacement field - reaches a critical value. In this work, we numerically investigate whether or not this rate may be reduced by applying an additional boundary load with a support disjoint from the support of the initial load f possibly responsible of the growth. We first introduce a well- posed relaxed formulation of this optimal location problem, and then compute explicitly the variation of the relaxed energy release rate with respect to the location of the additional force and also with respect to its intensity, taken into account the contact condition on the crack lips. Numerical simulations, based on a gradient descent method permit to optimize the support and amplitude of the extra load and so to reduce significantly the energy release rate. The optimal extra force highlights the balance between the opening and the in- plane shear modes. The case of a multi-crack structure is considered as well.

BIO:
Born in 1971, phD in Toulouse in 1998 on mortar methods for contact problems, assistant professor (permanent position) in University of Chambery from 1998 to 2002, habilitation in 2001, professor in University of Besancon since 2002.
Works especially on finite elements and contact and friction problems.

HOST: Prof. Rolf Krause

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