An overview of implicit and explicit phase field models for quasi-static failure processes, implementation and computational efficiency

•An overview of explicit and implicit phase field models details about their theories and implementation is presented.•A comprehensive comparation of the computational efficiency is made between the implicit and explicit phase field models.•Codes associated with the ABAQUS implementation through UEL/VUEL are provided.•A mass/viscosity scaling scheme for the explicit phase field model is presented to increase the critical stable time increment.•A non-iteration scheme for the implicit phase field model is introduced to eliminate the iteration. Phase field models have become a promising tool in modelling failure processes for various engineering applications. However, their computational inefficiency has posed challenges for a wider application which is desired in engineering. While most papers present implicit phase field models, only a few studies devoted to explicit phase field models have been reported in recent years and most papers report their high computational efficiency compared to implicit phase field models. The purpose of this contribution is to present an overview of the implicit and explicit phase field models for quasi-static failure processes, detailing about their theories and implementation in the commercial software ABAQUS. The provided ABAQUS implementation programs can serve as a numerical tool for modelling engineering problems. Several numerical examples are then presented and a comparison of their computational efficiency is subsequently provided. Moreover, a mass/viscosity scaling scheme for the explicit phase field model and a non-iteration scheme for the implicit phase field model are introduced both improve their efficiency. The comparison results clearly reveal that the computational efficiency can be improved significant by using the explicit phase field model, and more attention should be paid to it.