Abstract for May 9, 2006
Peter Philip (IMA and Corning):
A Quasistatic Crack Propagation Model Allowing for
Cohesive Forces and Crack Reversibility Using Local
While the classical theory of Griffith is the foundation of modern
understanding of brittle fracture, it has a number of significant
shortcomings: Griffith theory does not predict crack initiation and path
and it suffers from the presence of unphysical stress singularities.
In 1998, Francfort and Marigo presented an energy funtional minimization
method, where the crack (or its absence) as well as its path are part of
the problem's solution. The energy functionals act on spaces of functions
of bounded variations, where the cracks are related to the discontinuity
sets of such functions. The new model presented here uses modified energy
functionals to account for Barenblatt cohesive forces such that the model
becomes free of stress singularities. This is done in a physically
consistent way using recently published concepts of Sinclair. Here,
for the consistency of the model, it becomes necessary to allow for crack
reversibility and to consider local minimizers of the energy functionals.
The latter is achieved by introducing different time scales.
Finally, for some simple examples, the new model is solved and the
results are compared to corresponding results using previously existing
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