On the view of considering regularization parameter as material constant

In the fracture analysis of materials or structures 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. There is a powerful argument in the field of computational mechanics that regularization parameters should be regarded as material constants, and in many recently developed phase field models (PFMs), regularization parameters are used as material constants. In this paper, we derive a generalized form of a typical expression for the regularization parameter given as a material constant for making an in-depth analysis of the theoretical basis of such arguments, and estimate the rationality of this view through numerical analyses of some examples.