On the complementary roles of anisotropic crack density and anisotropic crack driving force in phase-field modeling of mixed-mode fracture

TL;DR

This study clarifies the distinct roles of anisotropic crack density and strain energy in phase-field fracture models, validated through experiments and parametric studies on different geometries.

Contribution

It systematically investigates and distinguishes how anisotropic crack density and strain energy influence fracture behavior in phase-field models, revealing their synergistic interaction.

Findings

Crack density anisotropy controls crack path and toughness.

Anisotropic strain energy influences crack deflection and stiffness.

Combined mechanisms produce nonlinear synergistic effects.

Abstract

Phase-field models for anisotropic fracture employ two complementary mechanisms: (i) the anisotropic crack density function, controlling direction-dependent fracture resistance, and (ii) the anisotropic strain energy, governing the fracture driving force. Although the unified framework was presented in Pranavi et al.[Comput. Mech., 73 (2024)], the distinct roles of these mechanisms and their interaction remain uninvestigated. This work addresses this gap by first validating the formulation against mixed-mode fracture experiments on a soft elastomer (Lu et al. [Extreme Mech. Lett., 48 (2021)]), and then conducting systematic parametric studies on single-edge-notched (SEN) and open-hole tension (OHT) specimens to isolate each mechanism. The SEN studies show that the crack density anisotropy controls the crack path and toughness while leaving the elastic response unchanged, whereas the anisotropic strain energy deflects the crack but saturates rapidly. The OHT studies reveal a geometry-dependent role expansion: the anisotropic strain energy governs fiber-orientation-dependent stiffness, peak force, and fracture displacement. When both mechanisms act together, the combined response exhibits nonlinear synergistic interaction exceeding the linear sum of the individual contributions. These results establish that the crack density anisotropy governs the crack path (fracture resistance), while the anisotropic strain energy governs the driving force and, in stress-concentration geometries, additionally controls the elastic strain energy distribution around the stress concentrator.