Crack Face Contact Modeling is Essential to Predict Crack-Parallel Stresses

TL;DR

This work tackles the inadequacy of common phase-field fracture energy splits to account for crack orientation, which can cause unphysical crack growth under crack-parallel stresses. It introduces a crack-orientation aware formulation that uses a QR decomposition of the deformation gradient in the crack-normal basis and an effective crack energy $W_d$ to distinguish crack-normal from crack-parallel modes, while allowing crack-face contact to behave like the intact material. Compared with Spectral and VolDev splits, the new model yields physically consistent stress fields and avoids spurious crack growth under crack-parallel loading, providing more reliable predictions for crack growth in applications where crack-parallel stresses are significant. The approach is formulated within a hyperelastic framework and implemented via FEM (FEniCS), with code available for replication and extension to more complex scenarios such as friction, poromechanics, and crack nucleation coupling.

Abstract

Phase-field fracture models provide a powerful approach to modeling fracture, potentially enabling the unguided prediction of crack growth in complex patterns. To ensure that only tensile stresses and not compressive stresses drive crack growth, several models have been proposed that aim to distinguish between compressive and tensile loads. However, these models have a critical shortcoming: they do not account for the crack direction, and hence they cannot distinguish between crack-normal tensile stresses that drive crack growth and crack-parallel stresses that do not. In this study, we apply a phase-field fracture model, developed in our earlier work, that uses the crack direction to distinguish crack-parallel stresses from crack-normal stresses. This provides a transparent energetic formulation that drives cracks to grow in when crack faces open or slide past each other, while the cracks respond like the intact solid when the crack faces contact under normal compressive loads. We compare our approach against two widely used approaches, Spectral splitting and the Volumetric-Deviatoric splitting, and find that these predict unphysical crack growth and unphysical stress concentrations under loading conditions in which these should not occur. Specifically, we show that the splitting models predict spurious crack growth and stress concentration under pure crack-parallel normal stresses. However, our formulation, which resolves the crack-parallel stresses from the crack-normal stresses, predicts these correctly.

Figures (7)

• Figure 1: The top row shows different loadings, and the middle and lower rows show the idealized deformation for intact and cracked specimens, respectively. Based on this idealization, we assign zero energy to modes (a) and (b). The dotted lines in the second and third row show the undeformed configuration. This decomposition follows steinke2019phasehakimzadeh2025phase.
• Figure 2: Comparison of crack growth paths and stress fields under tensile crack-parallel stress.
• Figure 3: Comparison of crack growth paths and stress fields under compressive crack-parallel stress.
• Figure 4: Comparison of stress fields and deformation without crack growth under compressive crack-parallel stress with $\nu>0$. Deformations are magnified $150\times$ for visualization.
• Figure 5: Comparison of stress fields and deformation without crack growth under compressive crack-parallel stress with $\nu<0$. Deformations are magnified $150\times$ for visualization.