Key effects and selections of model parameters in a strength-based phase field model and applications

Conventional phase field models are widely used to simulate brittle fracture, but cannot independently control fracture strength beyond uniaxial tension. To address this limitation, strength-based phase field formulations that incorporate prescribed strength surfaces have been proposed. However, most existing studies primarily emphasize the role of the strength surface in fracture initiation, while the resulting constitutive response and its dependence on model parameters remain insufficiently examined. In this work, a systematic investigation of the key model parameters (i.e. length scale, scaling factor, degradation function, and a newly introduced compression enhancement factor) is conducted through homogeneous solutions and parametric analyses. The results reveal that improper selection or inconsistent coupling of these parameters can lead to physically incorrect strength surfaces and constitutive laws. In particular, an inappropriate parameter combination may cause the predicted strength surface in the biaxial tension region to shrink toward the origin, implying an artificial reduction of admissible stress states. Moreover, when the compression enhancement factor is set to 1, the formulation degenerates to the revisited model used in publications, in which the compressive stress does not decrease after the peak stress, contradicting the typical softening response observed in brittle materials. By varying the compression enhancement factor, the strength surface can be tuned from a cone-like critical shape to an ellipsoid-like envelope, enabling flexible calibration to different material behaviors. The numerical results demonstrate that a combined examination of both the strength surface and the constitutive law is essential for ensuring physically admissible predictions of fracture initiation and propagation. The source code is available at https://github.com/MCMB-Lab/StrengthBasedPhaseFieldModel .