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

Abstract

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.

A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review

“…The phase field method (PFM) has become a popular numerical method for the analysis of the crack problems in recent years, since its implementation is free of crack tracking algorithms, enabling relatively easy simulation of complicated crack patterns, such as nucleation, branching, and coalescence [25][26][27][28]. The PFM, however, requires highly fine discretization due to the small length scale and becomes staggeringly computationalresource intensive as a result [29][30][31], severely limiting its application in actual industry. In addition, the PFM is usually incorporated with the finite element method (FEM) during implementation.…”

“…In addition, the PFM is usually incorporated with the finite element method (FEM) during implementation. Therefore, some computational issues of the FEM, such as sensitivity to geometry of the domain and size of discretization, also affect the PFM [31][32][33].…”

“…Among various numerical methods for the analysis of the crack problems to compute crack opening displacement, the boundary element method (BEM) is widely chosen, because it only discretizes boundaries of a domain of interest and consequently enables a more-efficient computation and a more-convenient implementation [34][35][36][37], while most of the other methods, such as the PFM or FEM, require discretization of the whole domain [31]. Furthermore, the BEM exploits existed analytical fundamental solutions, ensuring a potentially more accurate computation [38][39][40][41].…”