Advancements in Phase-Field Modeling for Fracture in Nonlinear Elastic Solids under Finite Deformations

The prediction of failure mechanisms in nonlinear elastic materials holds significant importance in engineering applications. In recent years, the phase-field model has emerged as an effective approach for addressing fracture problems. Compared with other discontinuous fracture methods, the phase-field method allows for the easy simulation of complex fracture paths, including crack initiation, propagation, coalescence, and branching phenomena, through a scalar field known as the phase field. This method offers distinct advantages in tackling complex fracture problems in nonlinear elastic materials and exhibits substantial potential in material design and manufacturing. The current research has indicated that the energy distribution method employed in phase-field approaches significantly influences the simulated results of material fracture, such as crack initiation load, crack propagation path, crack branching, and so forth. This impact is particularly pronounced when simulating the fracture of nonlinear materials under finite deformation. Therefore, this review outlines various strain energy decomposition methods proposed by researchers for phase-field models of fracture in tension–compression symmetric nonlinear elastic materials. Additionally, the energy decomposition model for tension–compression asymmetric nonlinear elastic materials is also presented. Moreover, the fracture behavior of hydrogels is investigated through the application of the phase-field model with energy decomposition. In addition to summarizing the research on these types of nonlinear elastic body fractures, this review presents numerical benchmark examples from relevant studies to assess and validate the accuracy and effectiveness of the methods presented.