Regularity for minimizers of the Griffith fracture energy

Abstract: The Griffith criterion says that the energy to crack a brittle elastic material is proportional to the length of the crack. Understanding the regularity of minimizers requires unraveling the complex interplay of bulk (elastic) and surface (crack) energies in the vectorial setting of linearized frame indifference. In dimension 2, we prove that the crack of a minimizer is given by a $C^{1,\alpha}$ surface outside of a singular set of points that has dimension strictly less than 1, analogous to results for the scalar Mumford-Shah functional. Joint work with Manuel Friedrich (FAU) and Camille Labourie (UPS).

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)