In the fracture analysis of materials including cracks, defects and voids, the phase field method is one of the most efficient and popular methods.
The phase field methods provide a stable and robust solution by regularizing the singularity of a mechanical system with discontinuities, and a regularization parameter is used for that.
The selection on regularization parameter has become so serious because the solution results by the phase field model have much greater dependence on regularization parameters than the size of elements or number of iterations.
There is a powerful argument in the field of computational mechanics that regularization parameters should be regarded as material constants.
In many recently developed phase field models (PFMs), regularization parameters are used as material constants, and many investigations have demonstrated that the accurate results are obtained by setting the regularization parameter as material constant.
We first verified that the expression for the regularization parameter should be expressed differently according to the energetic degradation function and crack geometric function on which the model is based.
We then extend the analytical solution of one-dimensional bar problem by the PFM based on the view of considering the regularization parameter as a material constant to derive a generalized formula for obtaining regularization parameters for the PFM using arbitrary energetic degradation functions and crack geometric functions.
Then, expressions for obtaining regularization parameters as material constants were presented in three typical cases.
And then, we examined whether the reasonable results were given for the two most typical fracture analysis problems, when using the regularization parameters obtained from these formulas.
Through the simulation analysis, it was found that the maximum load and crack path are not predicted correctly and that certain errors occur in all the examples if the regularization parameter is considered as a material constant.
Hence, we have reached the conclusion that the regularization parameter determined by material properties should be used with caution.
This conclusion, in contrast to the previous view that regularization parameters should be considered as material constants, will help to further refine the models by adding new viewpoints and insights to the researches of phase field methods.
The result has been published in the journal of "Mechanics Research Communication" (133, 2023) under the title of "On the view of considering regularization parameter as material constant" (https://doi.org/ j.mechrescom.2023.104196).
