Perturbed area functionals and brittle damage mechanics

Details Perturbed area functionals and brittle damage mechanics Perturbed area functionals and brittle damage mechanics

2005-11-09

arxiv.org/abs/math/0511240v1

Mathematics

Analysis of PDEs

Preprint IMAR no. 27/1996

Scientific paper

Some Mumford-Shah functionals are revisited as perturbed area functionals in connection with brittle damage mechanics. We find minimizers "on paper" for the classical Mumford-Shah functional for some particular two dimensional domains and boundary conditions. These solutions raise the possibility of validating experimentally the energetic model of crack appearance. Two models of brittle damage and fracture are proposed after; in the one of these models the crack belongs to the set of integral varifolds. We have felt the necessity to start the paper with a preliminary section concerning classical results in equilibrium of a cracked elastic body reviewed in the context of Sobolev spaces with respect to a measure. Further information at http://irmi.epfl.ch/cag/buliga_bfrac.html .

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