TY - JOUR

T1 - 3D phase-field cohesive fracture

T2 - Unifying energy, driving force, and stress criteria for crack nucleation and propagation direction

AU - Feng, Ye

AU - Hai, Lu

N1 - Publisher Copyright: © 2025 The Authors

PY - 2025/3

Y1 - 2025/3

N2 - This paper presents a 3D variational phase-field cohesive fracture model that incorporates crack direction information into the energy functional. Through an analytical homogenization procedure, the crack normal is obtained in closed form based on the principle of energy minimization. We find that, within the proposed model, several widely recognized crack direction criteria—including the minimum potential energy, maximum driving force, and maximum cohesive stress—are consistent and unified. The remaining criteria are simply stress-space descriptions of the same physical state, derived from the strain-space minimum potential energy criterion through the Legendre transformation. The performance of the proposed model is demonstrated through four representative numerical examples involving tension, torsion, anti-plane shear, and mixed-mode loading. The results indicate that, as the proposed model faithfully converges to the 3D cohesive zone model with a mixed-mode cohesive law, it is capable of predicting complex 3D crack morphologies during nucleation and growth, and is general enough to describe both tensile- and shear-dominated 3D fractures.

AB - This paper presents a 3D variational phase-field cohesive fracture model that incorporates crack direction information into the energy functional. Through an analytical homogenization procedure, the crack normal is obtained in closed form based on the principle of energy minimization. We find that, within the proposed model, several widely recognized crack direction criteria—including the minimum potential energy, maximum driving force, and maximum cohesive stress—are consistent and unified. The remaining criteria are simply stress-space descriptions of the same physical state, derived from the strain-space minimum potential energy criterion through the Legendre transformation. The performance of the proposed model is demonstrated through four representative numerical examples involving tension, torsion, anti-plane shear, and mixed-mode loading. The results indicate that, as the proposed model faithfully converges to the 3D cohesive zone model with a mixed-mode cohesive law, it is capable of predicting complex 3D crack morphologies during nucleation and growth, and is general enough to describe both tensile- and shear-dominated 3D fractures.

KW - 3D crack

KW - Cohesive fracture

KW - Crack direction

KW - Maximum driving force

KW - Mixed-mode fracture

KW - Phase-field model

KW - Variational principle

UR - http://www.scopus.com/inward/record.url?scp=85215408153&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2025.106036

DO - 10.1016/j.jmps.2025.106036

M3 - Article

AN - SCOPUS:85215408153

VL - 196

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

M1 - 106036

ER -