The Journal Club for April 2021 presents a concise review of the so-called variational phase-field fracture theory for brittle and cohesive fracture. Topics include the pioneering work of Griffith on brittle fracture in 1920, Barenblatt's cohesive zone model in 1959, to Marigo/Francfort's variational formulation of Griffith's brittle fracture 78 years later and the Bourdin's phase-field regularisation of MF's model. Also discussed is recent models for cohesive fracture, the role of the length scale parameter, solver for the coupled PDEs and some applications.
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