Abstract

Nonlinear finite element methods (NLFEM) have become indispensable for predicting structural failure in complex engineering systems, particularly where linear models fail to capture critical behaviors, such as large deformations, crack propagation, and post-buckling responses. This study investigates and compares several state-of-the-art NLFEM techniques – namely cohesive zone modeling (CZM), extended finite element method (XFEM), and phase-field fracture modelling – in the context of structural failure prediction. Three representative case studies are presented: (1) progressive collapse in a reinforced concrete frame, (2) interlaminar delamination in a composite laminate, and (3) post-buckling behavior in a thin-walled cylindrical shell. Quantitative results reveal that phase-field models achieved up to 18% higher crack path accuracy compared to XFEM in brittle fracture scenarios, while adaptive CZM implementations offered 25–30% reduction in computational time without compromising accuracy. The findings highlight the trade-offs between computational efficiency and damage resolution across different methods. Additionally, the study demonstrates that the choice of nonlinear modeling strategy significantly influences convergence behavior and mesh sensitivity, especially in high-gradient damage zones. By integrating comparative simulations and performance metrics, this work offers practical insights for selecting appropriate NLFEM techniques in structural mechanics applications involving failure analysis. The results provide a decision-making framework for researchers and engineers aiming to balance accuracy, robustness, and computational cost in advanced structural simulations.

Keywords:Nonlinear finite element method, structural failure prediction, constitutive modeling, damage and fracture mechanics, computational mechanics, data-driven simulation

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1. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. 2nd ed. Wiley; 2014.
2. Simo JC, Hughes TJR. Computational Inelasticity. Springer-Verlag; 1998.
3. Lemaitre J, Desmorat R. Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer; 2005.
4. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Meth Eng. 1999;46(1):131–50.
5. Miehe C, Hofacker M, Welschinger F. A phase field model for rate-independent crack propagation. Comput Methods Appl Mech Eng. 2010;199(45–48):2765–78.
6. Oliver J, Huespe AE, Pulido MD, Chaves EWA. From continuum damage mechanics to fracturing mechanics: the strong discontinuity approach. Comput Methods Appl Mech Eng. 2002;193(27–29):3087–120.
7. Bazant ZP, Planas J. Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press; 1997.
8. Rabczuk T. Computational methods for fracture in brittle and quasi-brittle solids: state-of-the-art review and future perspectives. ISRN Appl Math. 2013; 2013:849231.
9. Liu Y, Nagarajaiah S. Novel reduced-order model for nonlinear dynamic analysis using proper orthogonal decomposition. J Eng Mech. 2009;135(5):406–19.
10. Zhuang X, Chen L, Rabczuk T. Machine learning guided real-time failure prediction in complex structures. Eng Fract Mech. 2020; 224:106818.
11. Tejchman J, Wu W, Bauer E. Shear Localization in Granular Media: Modeling and Experiments. Springer; 2007.
12. Ghosh S, Kikuchi N. Adaptive finite element methods for modeling microstructure–property relationships in composite materials. Int J Numer Meth Eng. 1991;31(3):541–76.
13. Nguyen VP, Lloberas-Valls O, Stroeven M, Sluys LJ. Computational homogenization for multiscale crack modeling. Comput Methods Appl Mech Eng. 2012;200(37–40):3089–100.
14. Zienkiewicz OC, Taylor RL, Zhu JZ. The Finite Element Method: Its Basis and Fundamentals. 7th ed. Elsevier; 2013.

Abstract

Nonlinear finite element methods (NLFEM) have become indispensable for predicting structural failure in complex engineering systems, particularly where linear models fail to capture critical behaviors, such as large deformations, crack propagation, and post-buckling responses. This study investigates and compares several state-of-the-art NLFEM techniques – namely cohesive zone modeling (CZM), extended finite element method (XFEM), and phase-field fracture modelling – in the context of structural failure prediction. Three representative case studies are presented: (1) progressive collapse in a reinforced concrete frame, (2) interlaminar delamination in a composite laminate, and (3) post-buckling behavior in a thin-walled cylindrical shell. Quantitative results reveal that phase-field models achieved up to 18% higher crack path accuracy compared to XFEM in brittle fracture scenarios, while adaptive CZM implementations offered 25–30% reduction in computational time without compromising accuracy. The findings highlight the trade-offs between computational efficiency and damage resolution across different methods. Additionally, the study demonstrates that the choice of nonlinear modeling strategy significantly influences convergence behavior and mesh sensitivity, especially in high-gradient damage zones. By integrating comparative simulations and performance metrics, this work offers practical insights for selecting appropriate NLFEM techniques in structural mechanics applications involving failure analysis. The results provide a decision-making framework for researchers and engineers aiming to balance accuracy, robustness, and computational cost in advanced structural simulations.

Keywords:Nonlinear finite element method, structural failure prediction, constitutive modeling, damage and fracture mechanics, computational mechanics, data-driven simulation

🔒 This is a subscription article

Full text is available to subscribers and institutional members. Please choose an option below to access it.

1. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. 2nd ed. Wiley; 2014.
2. Simo JC, Hughes TJR. Computational Inelasticity. Springer-Verlag; 1998.
3. Lemaitre J, Desmorat R. Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer; 2005.
4. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Meth Eng. 1999;46(1):131–50.
5. Miehe C, Hofacker M, Welschinger F. A phase field model for rate-independent crack propagation. Comput Methods Appl Mech Eng. 2010;199(45–48):2765–78.
6. Oliver J, Huespe AE, Pulido MD, Chaves EWA. From continuum damage mechanics to fracturing mechanics: the strong discontinuity approach. Comput Methods Appl Mech Eng. 2002;193(27–29):3087–120.
7. Bazant ZP, Planas J. Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press; 1997.
8. Rabczuk T. Computational methods for fracture in brittle and quasi-brittle solids: state-of-the-art review and future perspectives. ISRN Appl Math. 2013; 2013:849231.
9. Liu Y, Nagarajaiah S. Novel reduced-order model for nonlinear dynamic analysis using proper orthogonal decomposition. J Eng Mech. 2009;135(5):406–19.
10. Zhuang X, Chen L, Rabczuk T. Machine learning guided real-time failure prediction in complex structures. Eng Fract Mech. 2020; 224:106818.
11. Tejchman J, Wu W, Bauer E. Shear Localization in Granular Media: Modeling and Experiments. Springer; 2007.
12. Ghosh S, Kikuchi N. Adaptive finite element methods for modeling microstructure–property relationships in composite materials. Int J Numer Meth Eng. 1991;31(3):541–76.
13. Nguyen VP, Lloberas-Valls O, Stroeven M, Sluys LJ. Computational homogenization for multiscale crack modeling. Comput Methods Appl Mech Eng. 2012;200(37–40):3089–100.
14. Zienkiewicz OC, Taylor RL, Zhu JZ. The Finite Element Method: Its Basis and Fundamentals. 7th ed. Elsevier; 2013.