Abaqus implementation of a phase field–cohesive zone fracture model for composite structures with an implicit scheme

Abstract Commercial and academic finite element software packages typically support either phase field modeling for bulk failure or cohesive zone modeling for interfacial damage. Still, an integrated and flexible framework that combines these two is not easily available in commercial software. This paper presents a phase field–cohesive zone (PF–CZ) model implemented in Abaqus, enabling simultaneous simulation of bulk and interfacial fracture within a single computational platform. This framework combines user-defined elements (UEL) for the phase field formulation that covers both brittle and ductile fractures in the bulk, and various Abaqus built-in cohesive elements with customizable traction–separation laws for the interface. A robust and implicit Newton–Raphson solution scheme combined with a staggered method is employed to solve phase and displacement unknowns, with detailed derivation of the stiffness and tangent stiffness matrices. Validation is performed via three-element tensile tests comparing results from Abaqus and MATLAB-based step-by-step calculations. The model is further demonstrated through simulations of bi-material interface fracture, ceramic matrix composite failure, and four-point bending of reinforced concrete beams. This work offers a verified and extensible framework for researchers and engineers who are new to either the phase field model or the cohesive zone model to study complex fracture scenarios in composite structures. In addition, the limitations of the phase field length scale parameter are analyzed and verified through simulation results. The source code is available at https://github.com/MCMB-Lab/AbaqusPF-CZmodel .

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Publication Details

Journal
Archive of Applied Mechanics
Published
2026-02-18
DOI
https://doi.org/10.1007/s00419-026-03031-6
Primary Topic
Numerical methods in engineering
Type
article
Field-Weighted Citation Impact
0.00

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article

Abaqus implementation of a phase field–cohesive zone fracture model for composite structures with an implicit scheme

Hsiao Wei Lee, Ahmad R. Najafi, Mohammad Irfan Iqbal, Alireza Ashkpour et al.
Archive of Applied Mechanics
Numerical methods in engineering
article

Abaqus implementation of a phase field–cohesive zone fracture model for composite structures with an implicit scheme

Hsiao Wei Lee, Ahmad R. Najafi, Mohammad Irfan Iqbal, Alireza Ashkpour, Christopher M. Sales, Li Meng, Yaghoob Amir Farnam, Mija H. Hubler
article en

Abstract

Abstract Commercial and academic finite element software packages typically support either phase field modeling for bulk failure or cohesive zone modeling for interfacial damage. Still, an integrated and flexible framework that combines these two is not easily available in commercial software. This paper presents a phase field–cohesive zone (PF–CZ) model implemented in Abaqus, enabling simultaneous simulation of bulk and interfacial fracture within a single computational platform. This framework combines user-defined elements (UEL) for the phase field formulation that covers both brittle and ductile fractures in the bulk, and various Abaqus built-in cohesive elements with customizable traction–separation laws for the interface. A robust and implicit Newton–Raphson solution scheme combined with a staggered method is employed to solve phase and displacement unknowns, with detailed derivation of the stiffness and tangent stiffness matrices. Validation is performed via three-element tensile tests comparing results from Abaqus and MATLAB-based step-by-step calculations. The model is further demonstrated through simulations of bi-material interface fracture, ceramic matrix composite failure, and four-point bending of reinforced concrete beams. This work offers a verified and extensible framework for researchers and engineers who are new to either the phase field model or the cohesive zone model to study complex fracture scenarios in composite structures. In addition, the limitations of the phase field length scale parameter are analyzed and verified through simulation results. The source code is available at https://github.com/MCMB-Lab/AbaqusPF-CZmodel .

Archive of Applied MechanicsVol. 96(3)
University of Colorado Boulder (US), Drexel University (US)
Drexel University, Defense Advanced Research Projects Agency
Sustainable cities and communities
Openalex Percentile: Top 51%
Numerical methods in engineering
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