# Criteria For The Computational Accuracy Of Phase Field Method Used In Analyzing The Fracture Process Of Material

2023.10.19.

The respected Comrade Kim Jong Un said:

"In scientific research, it should focus on satisfactorily resolving the theoretical and practical, scientific and technological problems arising in building a powerful socialist country, developing the sector of basic sciences and pushing back the frontiers of science and technology."

Structural failure is a challenging problem commonly encountered in engineering practice, and the application of the principles and theories of fracture mechanics or damage mechanics to numerical simulation methods based on computer is a very important issue at present. It has been extensively studied in the fields of mechanics and engineering since the end of the last century.

The phase field method has attracted extensive attention and has been applied to lots of fracture problems since complex crack problems can easily be solved by this method.

The phase field method based on crack diffusion concept does not directly describe the discontinuities in a discretized system, but can describe the fracture process without any crack tracking algorithm by diffusing the phase field variables representing the damage degree. The phase field method has emerged as one of the best recommended methods for numerical analysis of fracture problems in the field of computational mechanics since it can easily control the diffusion width of the crack and naturally describe such complex crack paths as multiple cracks or crack branching.

However, it is difficult to predict accurately the maximum load-carrying capacity by this method in fracture analysis. To address this issue, there have been numerous studies to develop energy degradation functions and crack geometric functions required in constructing the phase field models.

It has been demonstrated that the energy degradation functions and crack geometric functions used in phase field models have great influence on the simulation results, but combination of these newly developed functions does not always lead to an excellent phase field model.

During further research on the material fracture analysis using the phase field model, we have developed three new criteria that energetic degradation functions and crack geometric functions should satisfy.

We have analyzed all phase field models constructed by a possible combination of energy degradation and crack geometric functions studied so far.

We have found that only the model satisfying the three criteria are scarcely dependent on regularization parameter and accurate and stable in calculation of maximum load and crack path.

The results were published in the SCI journal "Engineering Fracture Mechanics" under the title of "Three criteria for ensuring computational accuracy in phase field modelling" (https:// doi.org/10.1016/j.engfracmech.2022.108289).