Variational fracture: twenty years after

Abstract

In this work, we propose to succinctly review, in non technical terms, the current mathematical state of brittle fracture first put forth by A. A. Griffith in his seminal work Griffith (Philos Trans R Soc Lond CCXXI-A:163–198, 1920), then re-interpreted under the label “variational fracture” in Francfort and Marigo (J. Mech Phys Solids 46(8):1319–1342, 1998). and subsequent works. We will only address the sharp theory and will limit ourselves to a theoretical exposition, leaving phase-field approximations and other possible implementations to other articles within this volume.