Free discontinuity problems and variational models in fracture mechanics

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Project objective

One direction of research will focus on the possibility of defining spaces of discontinuous functions with suitable compactness properties, where variational problems can be handled which take into account elastic deformation, cavitation, fracture initiation and crack deformation. On these spaces functionals will be investigated, which describe the energies of fractured bodies, and the solution of some problems in the mechanics of brittle hyperelastic materials will be seeked. We will confront the De Giorgi-Ambrosio SBV-functions approach to problems in fracture mechanics, and the M\uller-Spector penalized perimeters approach to cavitation, under the common viewpoint of Federer's currents. An other direction of research will be the description of problems in fracture mechanics through an approximation scheme by smooth functionals of non-local character, using the methods of r-convergence and recent results on quasiconvex functions. A mechanical interpretation of this approximation will be studied, investigating the possibility of understanding the non-local interactions as small-scale effects of interatomic forces, looking for possible links with singular perturbations approaches."

Original text from CORDIS.

Participants

• MAX-PLANCK-GESELLSCHAFT ZUR FOERDERUNG DER WISSENSCHAFTEN E.V. · MUENCHENCoordinatorGermany
• Not availableCity levelItaly

Links

• View on CORDIS