Numerical Modeling For Fracture Mechanics Problems Using The Open-source Fenics Platform

Caio César Prates Martins; Brenda Resende Lemos; Jean Pierre de Oliveira Bone; André Gustavo de Souza Galdino; Rodolfo Giacomim Mendes de Andrade

Caio César Prates Martins Federal Institute of Espírito Santo https://orcid.org/0009-0009-0609-200X
Brenda Resende Lemos Federal Institute of Espírito Sant
Jean Pierre de Oliveira Bone Federal Institute of Espírito Santo
André Gustavo de Souza Galdino Federal Institute of Espírito Sant https://orcid.org/0000-0002-5990-0287
Rodolfo Giacomim Mendes de Andrade Federal Institute of Espírito Santo https://orcid.org/0000-0003-3956-5941

Keywords: Numerical Modeling, FEniCS, Finite Elements, Fracture Mechanics

Abstract

Fracture mechanics is the mechanical approach to fracture processes, which emerged due to limitations in the application of traditional concepts of Mechanics of Materials to predict the behavior of cracked materials. Analytical problem solutions with this approach may be unattainable, which allows the use of numerical modeling, such as the finite element method. However, the use of more advanced software that solves engineering problems numerically is limited by its high cost. FEniCS is an open source computational platform that solves partial differential equations by the finite element method. Thus, from a tutorial for this computational platform, this work proposes to reproduce a classic problem of linear elastic fracture mechanics, based on the validation of a comparison of a linear elastic problem with the commercial software ANSYS ®. With the help of the provided tutorial, an code was built to model a three-point bending test. Implemented with the aid of Gmsh and Paraview, it was possible to obtain satisfactory results, and to show that FeniCS is a powerful and accessible tool for solving fracture mechanics problems.

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References

T. R. Chandrupatla and A. D. Belegundu, "Elementos Finitos," 4° ed., Pearson, 2014.

Ansys ® [Ansys Student], Version 2022, Ansys, Inc.

M. S. Alnaes et al., "The FEniCS Project Ver. 1.5," Archive of Numerical Software, vol. 3, 2015.

T. L. Anderson, "Fracture Mechanics - Fundamentals and Applications," 2nd Edition, CRC Press, 1994.

K. Majidzadeh, E. M. Kauffmann, and D. V. Ramsamooj, "Application of Fracture Mechanics in the Analysis of Pavement Fatigue," in Association of Asphalt Paving Technologists Proceedings, pp. 227-246, 1971.

G. Clerc, A. J. Brunner, P. Niemz, and J. Kuilen, "Application of Fracture Mechanics to Engineering Design of Complex Structures," in 1st Virtual European Conference on Fracture, Procedia Structural Integrity, vol. 28, pp. 1761-1767, 2020.

G. J. Neate, G. M. Sparkes, H. D. Williams, and A. T. Stewart, "Application of Fracture Mechanics to Industrial Problems," in Fracture Mechanics, Pergamon, pp. 69-90, 1979.

J. A. L. Rocha, "Termodinâmica da Fratura: Uma Nova Abordagem do Problema da Fratura nos Sólidos," EDUFBA, 2010.

P. T. R. Mendonça and E. A. Fancello, "O Método dos Elementos Finitos Aplicado à Mecânica dos Sólidos," 1st Edition, Orsa Maggiore, 2019.

Ansys ®, "Simulation Is a Superpower," Available: https://acortar.link/Xy7AhA. [Accessed: May. 14, 2023].

H. P. Langtangen and A. Logg, "Solving PDEs in Python: The FEniCS Tutorial 1," Simula Research Laboratory and Department of Informatics, University of Oslo, 2017.

E. M. Pañeda and H. Hirshikesh, "Phase Field Fracture Implementation in FEniCS," ResearchGate, 2020.

M. Ambati, T. Gerasimov, and L. De Lorenzis, "A Review on Phase-Field Brittle Models of Fracture and a New Fast Hybrid Formulation," Comput Mech, vol. 55, pp. 383-405, 2015.

J. Amor, J. Marigo, and C. Maurini, "Regularized Formulation of the Variational Brittle Fracture with Unilateral Contact: Numerical Experiments," Journal of the Mechanics and Physics of Solids, vol. 57, pp. 1209-1229, 2009.

C. Miehe, M. Hofacker, and F. Welschinger, "A Phase Field Model for Rate-Independent Crack Propagation: Robust Algorithmic Implementation Based on Operator Splits," Comput Methods Appl Mech Eng, vol. 199, pp. 2765-2778, 2010.

C. Geuzaine and J. Remacle, "Gmsh: A 3-D Finite Element Mesh Generator with Built-in Pre- and Post-Processing Facilities," International Journal for Numerical Methods in Engineering, vol. 79, pp. 1309-1331, 2009

J. Ahrens, B. Geveci, and C. Law, "Paraview: An End-user Tool for Large Data Visualization," in Visualization Handbook, Elsevier, pp. 978-0123875822, 2005

H. Hirshikesh, S. Natarajan and R. K. Annabattula, "A FEniCS Implementation of the Phase Field Method for Quasi-Static Brittle Fracture," Frontiers of Structural and Civil Engineering, vol. 13, 2019.