Shearlet approximation of brittle fracture evolutions (C03* [A10])

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A brittle material, subjected to a force, first deforms itself elastically, then it breaks without any intermediate phase. A model of brittle fractures was proposed by Francfort and Marigo, where the material displacement is typically a smooth function except on a relatively smooth jump set determining the fracture. This approach has the advantage not to require a pre-defined crack path, but has the drawback that any mesh discretization is a geometrical bias. Differently from finite elements, shearlets are frames with rotation invariance and optimal nonlinear approximation properties for the class of typical solutions of the brittle fracture model. The main goal of the project is the robust numerical simulation of brittle fractures, implementing a provably convergent and geometrically unbiased adaptive frame scheme based on shearlet discretizations.