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/