A simple and efficient implementation of explicit phase field method in ABAQUS to address complex three-dimensional fracture problems

The phase field method can analyze intricate crack growth behavior based on a regularized variational framework. However, its adaptation for solving complex three-dimensional fracture problems is still a challenge mainly due to the difficulties in numerical implementation and the corresponding high computational cost. In this study, a new ABAQUS implementation of explicit phase field method is proposed. The phase field was analogized to the temperature field, and the transient thermal variables in the heat transfer equation were rederived based on the explicit phase field governing equation. The dissipated inelastic energy was leveraged to characterize the volumetric heat flux, allowing the temperature field to be updated. To ensure the numerical stability, a series of novel formulations were proposed to restrict the temperature field rate. Finally, the field variables update approaches were described and the determination of critical time increment was discussed. Using this approach, the mechanical and thermal behaviors can be defined within a single user-defined material (VUMAT) subroutine. This implementation allows for convenient utilization of most built-in functions. Two classic brittle fracture examples were simulated firstly to test the efficiency of the proposed implementation through comparison with the UMAT implicit implementation, including comparison of computational time under different processors. Then the proposed implementation was exploited to solve several complex three-dimensional quasi-brittle fracture problems, and the corresponding predicted crack pattern and load-displacement data were compared with the experimental ones to validate the accuracy of the suggested model. The results revealed that the proposed explicit implementation is significantly more efficient than the implicit implementation of phase field, while maintaining the same accuracy. This approach can be leveraged to solve complex three-dimensional fracture problems considering mode I, mixed mode I + II and mixed mode I + III failure within an acceptable computational time. The proposed framework shows promise for efficient simulation of complex brittle/quasi-brittle fracture behavior in structural components. The source code is provided (https://github.com/xuanyge/Explicit-PFM-VUMAT.git) to enable interested researchers to utilize and implement it.