Three-layer phase-field model of finite strain shell for simulating quasi-static and dynamic fracture of elasto-plastic materials

•A new three-layer phase-field model for elasto-plastic materials based on the crack regularized phase-field model is proposed.•Five typical numerical examples are solved by the proposed phase-field model.•The three-layer phase-field model can better explain the differences in the response of thick-walled shells on different layers under quasi-static and dynamic loading in the thickness direction. Shell structures are widely used in the aerospace, automobile, pipeline, and construction industries. Under quasi-static and dynamic loading, the failure modes of the thin and thick shells are quite different. To explain the correct fracture behavior of the moderated thick shell under bending loads, this paper proposed a new three-layer phase-field model for elasto-plastic materials based on the crack regularized phase-field model. Three independent phase-fields corresponding to the shell’s upper, middle, and lower surfaces are used. This provides a realistic behavior in bending-dominated problems, which is illustrated in the classical beam and plate problems. Five typical numerical examples are given, including the bending of bi-clamped beam, the Muscat-Fenech and Atkins plate problem, the dynamic crack growth problem in a stiffened cylinder under internal pressure, the radial cracks problem in perforated sheets, and the circular steel plate subjected to an underwater blast load. All the problems have been successfully solved, and the proposed phase-field model is proved to be effective.