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

• Subject Area: Mathematics
• Term: from 2016 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 195170736

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.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 109: Discretisation in Geometry and Dynamics
• Applicant Institution: Technische Universität Berlin
• Project Heads: Professor Dr. Massimo Fornasier; Professorin Dr. Gitta Kutyniok