A concise review of small-strain phase-field modeling of ductile fracture

The computational modeling of ductile fracture is a complex problem due to the simultaneous presence of various competing dissipation mechanisms at the microscale resulting in evolving displacement discontinuities at the macroscale. Phase-field modeling of brittle fracture has emerged as one of the more computationally efficient smeared approaches for simulating crack propagation in solids. In recent years, there has been significant attention towards extending this approach to ductile fracture. The first papers on this topic were published approximately a decade ago, and since then, there has been a growing number of new contributions proposing different approaches and applications. The purpose of this work is to offer an extensive bibliography on phase-field modeling of ductile fracture, together with a concise presentation of some of the most widely used formulations, specifically limited to small-strain plasticity under monotonic loading. Few aspects of particular interest are also discussed in detail.