Convergence Check Phase-Field Scheme for Modelling of Brittle and Ductile Fractures

Abstract

The paper proposes a novel staggered phase-field framework for modelling brittle and ductile fractures in monotonic and cyclic loading regimes. The algorithm consists of two mesh layers (displacement and phase field) and a single special-purpose, user-defined finite element, which controls global convergence of the coupled problem and passing of the solution variables between mesh layers. The proposed algorithm is implemented into FE software ABAQUS. For the problem of high cyclic fatigue, a cycle-skipping scheme is also introduced. The proposed methodology is verified on the usual benchmark examples. Small-strain theory is applied, but it has been demonstrated that extension to large strains is straightforward using only the ABAQUS built-in option. The efficiency and stability of the proposed framework was proven by comparison of computational time and the number of iterations per increment in the RCTRL scheme.