Comptes Rendus
Short paper
Data-driven model based on the simulation of cracking process in brittle material using the phase-field method in application
Comptes Rendus. Mécanique, Volume 348 (2020) no. 8-9, pp. 729-744.

Numerical simulations and parametric studies of notched rectangular specimens subjected to dynamic tensile loads were performed. The simulations were based on two-dimensional finite element analysis to predict the brittle fracture path using the phase-field approach. The parametric studies investigated the influence of geometric parameters and the loading speed on crack path propagation. An empirical model based on the sparse proper generalized decomposition learning technique was created to predict the crack path. This model provides a quick prediction of the global behavior of the crack path circumventing the CPU cost of the full finite element method simulation.

Received:
Revised:
Accepted:
Online First:
Published online:
DOI: 10.5802/crmeca.52
Keywords: Dynamic fracture propagation, Finite element, Brittle fracture, Phase-field approach, s-PGD technique
Yosra Kriaa 1; Amine Ammar 2; Bassem Zouari 1

1 LA2MP Laboratory, University of Sfax, National Engineering School of Sfax, Tunisia
2 Arts et Metiers Institute of Technology, LAMPA, HESAM Université, F-49035 Angers, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{CRMECA_2020__348_8-9_729_0,
     author = {Yosra Kriaa and Amine Ammar and Bassem Zouari},
     title = {Data-driven model based on the simulation of cracking process in brittle material using the phase-field method in application},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {729--744},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {348},
     number = {8-9},
     year = {2020},
     doi = {10.5802/crmeca.52},
     language = {en},
}
TY  - JOUR
AU  - Yosra Kriaa
AU  - Amine Ammar
AU  - Bassem Zouari
TI  - Data-driven model based on the simulation of cracking process in brittle material using the phase-field method in application
JO  - Comptes Rendus. Mécanique
PY  - 2020
SP  - 729
EP  - 744
VL  - 348
IS  - 8-9
PB  - Académie des sciences, Paris
DO  - 10.5802/crmeca.52
LA  - en
ID  - CRMECA_2020__348_8-9_729_0
ER  - 
%0 Journal Article
%A Yosra Kriaa
%A Amine Ammar
%A Bassem Zouari
%T Data-driven model based on the simulation of cracking process in brittle material using the phase-field method in application
%J Comptes Rendus. Mécanique
%D 2020
%P 729-744
%V 348
%N 8-9
%I Académie des sciences, Paris
%R 10.5802/crmeca.52
%G en
%F CRMECA_2020__348_8-9_729_0
Yosra Kriaa; Amine Ammar; Bassem Zouari. Data-driven model based on the simulation of cracking process in brittle material using the phase-field method in application. Comptes Rendus. Mécanique, Volume 348 (2020) no. 8-9, pp. 729-744. doi : 10.5802/crmeca.52. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.52/

[1] T. Bhattacharjee; M. Barlingay; H. Tasneem; E. Roan; K. Vemaganti Cohesive zone modeling of mode I tearing in thin soft materials, J. Mech. Behav. Biomed. Mater., Volume 28 (2013), pp. 37-46 | DOI

[2] T. Bhattacharjee “Cohesive zone modeling of tearing in soft materials”, Master’s thesis, University of Cincinnati (2011)

[3] M. Barlingay “Modeling and simulation of tissue tearing and failure for surgical applications”, Master’s thesis, University of Cincinnati (2012)

[4] X.-P. Xu; A. Needleman Numerical simulations of fast crack growth in brittle solids, J. Mech. Phys. Solids, Volume 42 (1994) no. 9, pp. 1397-1434 | DOI | Zbl

[5] N. Moes; T. Belytschko Extended finite element method for cohesive crack growth, Eng. Fract. Mech., Volume 69 (2002) no. 7, pp. 813-833 | DOI

[6] J.-H. Song; H. Wang; T. Belytschko A comparative study on finite element methods for dynamic fracture, Comput. Mech., Volume 42 (2008) no. 2, pp. 239-250 | DOI | Zbl

[7] R. Borst Damage, material instabilities, and failure, Encyclopedia of Computational Mechanics, Vol. II, Wiley, 2004, pp. 335-375

[8] M. J. Borden Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture, Ph.D. thesis, The University of Texas at Austin (2012)

[9] M. J. Borden; C. V. Verhoosel; M. A. Scott; T. J. Hughes; C. M. Landis A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Eng., Volume 217–220 (2012), pp. 77-95 | DOI | MR | Zbl

[10] M. Wheeler; T. Wick; W. Wollner An augmented-lagrangian method for the phase-field approach for pressurized fractures, Comput. Methods Appl. Mech. Eng., Volume 271 (2014), pp. 69-85 | DOI | MR | Zbl

[11] B. Bourdin; G. A. Francfort; J.-J. Marigo Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, Volume 48 (2000) no. 4, pp. 797-826 | DOI | MR | Zbl

[12] G. A. Francfort; J.-J. Marigo Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, Volume 46 (1998) no. 8, pp. 1319-1342 | DOI | MR | Zbl

[13] B. Bourdin; C. J. Larsen; C. L. Richardson A time-discrete model for dynamic fracture based on crack regularization, Int. J. Fract., Volume 168 (2011) no. 2, pp. 133-143 | DOI | Zbl

[14] C. Miehe; F. Welschinger; M. Hofacker Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field implementations, Int. J. Numer. Methods Eng., Volume 83 (2010) no. 10, pp. 1273-1311 | DOI | MR | Zbl

[15] C. Miehe; M. Hofacker; F. Welschinger A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Comput. Methods Appl. Mech. Eng., Volume 199 (2010) no. 45, pp. 2765-2778 | DOI | MR | Zbl

[16] H. Jeong; S. Signetti; T. Seok Han; S. Ryu Phase field modeling of crack propagation under combined shear and tensile loading with hybrid formulation, Comput. Mater. Sci., Volume 155 (2018), pp. 483-492 | DOI

[17] M. Ambati; T. Gerasimov; L. De Lorenzis A Review on Phase-Field Models of Brittle Fracture and A New Fast Hybrid Formulation, Springer-Verlag, Berlin, Heidelberg, 2014 | Zbl

[18] C. Miehe; L.-M. Schanzel Phase field modeling of fracture in rubbery polymers. Part I: Finite elasticity coupled with brittle failure, J. Mech. Phys. Solids, Volume 65 (2014), pp. 93-113 | DOI | MR | Zbl

[19] C. Miehe; M. Hofacker; L.-M. Schaenzel; F. Aldakheel Phase field modeling of fracture in multi-physics problems. Part II: coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic plastic solids, Comput. Methods Appl. Mech. Eng., Volume 294 (2015), pp. 486-522 | DOI | MR | Zbl

[20] Z. A. Wilson; M. J. Borden; C. M. Landis A phase-field model for fracture in piezoelectric ceramics, Int. J. Fract., Volume 183 (2013) no. 2, pp. 135-153 | DOI

[21] T. Kirchdoerfer; M. Ortiz Data-driven computational mechanics, Comput. Methods Appl. Mech. Eng., Volume 304 (2016), pp. 81-101 | DOI | MR | Zbl

[22] T. Kirchdoerfer; M. Ortiz Data driven computing with noisy material data sets, Comput. Methods Appl. Mech. Eng., Volume 326 (2017), pp. 622-641 | DOI | MR | Zbl

[23] S. L. Brunton; J. L. Proctor; J. N. Kutz Discovering governing equations from data by sparse identifcation of nonlinear dynamical systems, Proc. Natl Acad. Sci. USA, Volume 113 (2016) no. 15, pp. 3932-3937 | DOI | Zbl

[24] S. L. Brunton; J. L. Proctor; J. N. Kutz Sparse identifcation of nonlinear dynamics with control, IFAC, Volume 49 (2016) no. 18, pp. 710-715

[25] M. Quade; M. Abel; J. N. Kutz; S. L. Brunton Sparse identifcation of nonlinear dynamics for rapid model recovery, Chaos, Volume 28 (2018) no. 6 (063116, 10 pages) | DOI

[26] D. Gonzalez; F. Chinesta; E. Cueto Termodynamically consistent data-driven computational mechanics, Contin. Mech. Termodyn. (2018) (in press, doi:10.1007/s00161-018-0677-z, hal-0182995)

[27] N. M. Mangan; S. L. Brunton; J. L. Proctor; J. N. Kutz Inferring biological networks by sparse identifcation of nonlinear dynamics, IEEE Trans. Mol. Biol. Multi-Scale Commun., Volume 2 (2016) no. 1, pp. 52-63 | DOI

[28] J. Mann; J. N. Kutz Dynamic mode decomposition for fnancial trading strategies, Quant. Finance, Volume 16 (2016) no. 11, pp. 1643-1655 | DOI | Zbl

[29] F. Chinesta; A. Ammar; E. Cueto Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models, Arch. Comput. Methods Eng.: State-of-the-Art Reviews, Volume 17 (2010) no. 4, pp. 327-350 | DOI | MR | Zbl

[30] F. Chinesta; R. Keunings; A. Leygue The Proper Generalized Decomposition for Advanced Numerical Simulations, Springer Briefs in Applied Sciences and Technology, Springer, Cham, 2014 | DOI | Zbl

[31] F. Chinesta; P. Ladeveze Separated Representations and PGD-Based Model Reduction, CISM International Centre for Mechanical Sciences, Courses and Lectures, vol. 554, Springer, Vienna, 2014 | DOI | Zbl

[32] D. Gonzalez; A. Ammar; F. Chinesta; E. Cueto Recent advances on the use of separated representations, Int. J. Numer. Methods Eng., Volume 81 (2010) no. 5, pp. 637-659 | DOI | MR | Zbl

[33] A. Badas; D. Gonzalez; I. Alfaro; F. Chinesta; E. Cueto Local proper generalized decomposition, Int. J. Numer. Methods Eng., Volume 112 (2017) no. 12, pp. 1715-1732 | DOI | MR

[34] E. Cueto; D. Gonzalez; I. Alfaro Proper Generalized Decompositions, Springer Briefs in Applied Sciences and Technology, Springer, Cham, 2016 | DOI

[35] D. Gonzalez; A. Badas; I. Alfaro; F. Chinesta; E. Cueto Model order reduction for real-time data assimilation through extended Kalman flters, Comput. Methods Appl. Mech. Eng., Volume 326 (2017), pp. 679-693 | DOI

[36] R. Ibáñez; E. Abisset-Chavanne; A. Ammar; D. González; E. Cueto; A. Huerta; J. L. Duval; F. Chinesta A multidimensional data-driven sparse identification technique: The sparse proper generalized decomposition, Hindawi Complexity (2018), pp. 1-11 (doi:10.1155/2018/5608286) | Zbl

[37] B. Bourdin; G. A. Francfort; J. J. Marigo The Variational Approach to Fracture, Springer, Berlin, 2008 | DOI | Zbl

[38] C. Miehe; M. Hofacker; F. Welschinger A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Comput. Methods Appl. Mech. Eng., Volume 199 (2010) no. 45–48, pp. 2765-2778 | DOI | MR | Zbl

Cited by Sources:

Comments - Policy


Articles of potential interest

A possible link between brittle and ductile failure by viewing fracture as a topological defect

Amit Acharya

C. R. Méca (2020)


Lipschitz regularization for softening material models: the Lip-field approach

Nicolas Moës; Nicolas Chevaugeon

C. R. Méca (2021)


Fracture and permeability of concrete and rocks

Gilles Pijaudier-Cabot

C. R. Phys (2020)