Abaqus implementation of the phase-field approach to fracture
Abstract
In this paper, we introduce an Abaqus user-subroutine implementation of the phase-field model of fracture initiated by Kumar, Francfort, and Lopez-Pamies (\emph{J. Mech. Phys. Solids} 112, 523--551, 2018). The implementation is presented for the basic case of isotropic linear elastic brittle materials with a Drucker-Prager strength surface. The material inputs are therefore the Young's modulus E, the Poisson's ratio ν, the uniaxial tensile strength sts, the uniaxial compressive strength scs, and the fracture toughness Gc. The mathematical correspondence between the heat equation and the evolution equation for the phase field v(bfX,t) is exploited through a UMAT subroutine, wherein the driving force ce(bfX,t) --- accounting for the material strength surface --- in the phase-field model plays the role of a heat source. To ensure that the equations for the displacement field bfu(bfX,t) and the phase field v(bfX,t) are solved in a staggered manner --- a solution strategy that, as opposed to monolithic approaches, reliably yields the correct physical solution --- we make use of a combination of UEXTERNALDB, UAMP, MPC, and URDFIL subroutines. Within this approach, the MPC and URDFIL subroutines are additionally utilized to enforce the required bounding and irreversibility inequalities on v(bfX,t) via a primal-dual active set approach. The capabilities and robustness of the proposed implementation are demonstrated by simulating the ``Nine Circles of Elastic Brittle Fracture'' on a silicate glass --- a set of tests that span the entire range of well-settled experimental knowledge on fracture nucleation and propagation. These simulations also serve to illustrate the deployment of the code using several native Abaqus finite elements, including the simplicial elements CPS3, CAX3, and C3D4.
Related
- Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials
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- Fracture-Bench: A Controlled Benchmark Suite for Machine Learning Surrogates in Phase-Field Fracture Mechanics
- A deep energy method formulation for phase-field modelling of ductile fracture
- Coupled Phase-Field Fracture and Discrete Dislocation Dynamics for Short-Crack Propagation
BibTeX
@misc{zhou2026abaqus,
title = {{Abaqus implementation of the phase-field approach to fracture}},
author = {Jiangwei Zhou and Victor Lefevre and Oscar Lopez-Pamies},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24820},
eprint = {2610.24820},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24820},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Abaqus implementation of the phase-field approach to fracture
AU - Jiangwei Zhou
AU - Victor Lefevre
AU - Oscar Lopez-Pamies
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24820
UR - https://arxiv.org/abs/2610.24820
AB - In this paper, we introduce an Abaqus user-subroutine implementation of the phase-field model of fracture initiated by Kumar, Francfort, and Lopez-Pamies (\emph{J. Mech. Phys. Solids} 112, 523--551, 2018). The implementation is presented for the basic case of isotropic linear elastic brittle materials with a Drucker-Prager strength surface. The material inputs are therefore the Young's modulus E, the Poisson's ratio ν, the uniaxial tensile strength sts, the uniaxial compressive strength scs, and the fracture toughness G_c. The mathematical correspondence between the heat equation and the evolution equation for the phase field v(bfX,t) is exploited through a UMAT subroutine, wherein the driving force c_e(bfX,t) --- accounting for the material strength surface --- in the phase-field model plays the role of a heat source. To ensure that the equations for the displacement field bfu(bfX,t) and the phase field v(bfX,t) are solved in a staggered manner --- a solution strategy that, as opposed to monolithic approaches, reliably yields the correct physical solution --- we make use of a combination of UEXTERNALDB, UAMP, MPC, and URDFIL subroutines. Within this approach, the MPC and URDFIL subroutines are additionally utilized to enforce the required bounding and irreversibility inequalities on v(bfX,t) via a primal-dual active set approach. The capabilities and robustness of the proposed implementation are demonstrated by simulating the ``Nine Circles of Elastic Brittle Fracture'' on a silicate glass --- a set of tests that span the entire range of well-settled experimental knowledge on fracture nucleation and propagation. These simulations also serve to illustrate the deployment of the code using several native Abaqus finite elements, including the simplicial elements CPS3, CAX3, and C3D4.
ER -