A variational approach to brittle damage and fracture
by
Gilles Francfort
AEB350, 3:15pm Monday, April 29, 1996
Abstract
This report is on joint work with I. Fonseca and J.J. Marigo.
I wish to propose a unified approach to the quasistatic evolution of
both fracture and damage in an elastic medium. The basic idea is as
follows:
1. When a crack, or a region with weaker stiffness appears or grows,
a certain amount of energy is released,
2. At the same time the elastic energy is modified,
3. Among all possible configurations of the cracks and/or of the
weakened region the material will choose, at any given time, that
(or those) which minimize the total energy (elastic + released -
work of external loads). This is of course just a postulate, but
such global stability criteria are very common in continuum
mechanics.
I show how such an approach leads to a relaxed formulation for the
evolution of the crack and/or damaged zone.
The damage process is characterized by a local volume fraction of
damaged material, together with (a) subscale microstructure(s). The
location and shapes of the crack(s) is a product of the analysis, and
no preexisting crack(s) is(are) needed. The relaxed formulation shows
the absence of interaction between the fracture and damaging processes.
In the context of fracture only a numerical algorithm is presented.
Computations performed by B. Bourdin are shown in an antiplane setting.
Numerical computations performed by J.M. Rossi in the context of damage
only are also presented.
Requests for preprints and reprints to: francfor@math.utah.edu
This source can be found at http://www.math.utah.edu/research/