The scaler value, \(\varphi\), which implies the crack phase-field parameter and alters slightly from 0 (completely intact state) to 1 (fully broken). The fracture behavior of phase-field fracture models is mainly adjusted by two parameters. The cracking resistance\(\mathcal{G}_{c}\ \)is a material parameter, which is a measure for the surface or fracture energy, needed to create new fracture surfaces. The second parameter is a length scale, which primarily controls the width of the transition zone between broken and undamaged material.
The stress degradation function,\(g:\left[0,1\right]\rightarrow[0,1]\)performs a key role in the formulation because it regulates how the stress reacts to alterations in the phase-field. A basic quadratic degradation function, which is prevalent in literature is,27