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A comparison between some fracture modelling approaches in 2D LEFM using finite elements

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Abstract

The finite element method has been widely used to solve different problems in the field of fracture mechanics. In the last two decades, new methods have been developed to improve the accuracy of the solution in 2D linear elastic fracture mechanics problems, such as the extended finite element method (XFEM) or the phantom node method (PNM). The goal of this work is to quantify the differences between some numerical approaches: standard finite element method (FEM), mechanical property degradation, interelemental crack method with multi-point constraints, XFEM and PNM. We explain the different techniques analysed together with their advantages and disadvantages. We compare these numerical techniques to model fracture using problems of reference with known solutions, evaluating their behaviour in terms of convergence with respect to the element size and accuracy of the stress intensity factor (SIF), stresses ahead the crack tip and crack propagation prediction. Some of the new techniques have shown a better accuracy in SIF calculation or stress fields ahead the crack tip and other lead to high errors in local results estimations. However, all methods reviewed here can predict crack propagation for the problems of reference of this work, showing good accuracy in crack orientation prediction.

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References

  • Agwai A, Guven I, Madenci E (2010) Comparison of XFEM, CZM and PD for predicting crack initiation and propagation. In: Collection of technical papers—AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference

  • Areias PMA, Belytschko T (2005) Analysis of three-dimensional crack initiation and propagation using the extended finite element method. Int J Numer Methods Eng 63(8):760–788

    Article  Google Scholar 

  • Argyris JH, Kelsey S (1954) Energy theorems and structural analysis. Aircraft Eng 26(12):410–422

    Article  Google Scholar 

  • Banks-Sills L (1991) Application of the finite element method to linear elastic fracture mechanics. Appl Mech Rev 44(10):447–461

    Article  Google Scholar 

  • Banks-Sills L, Sherman D (1986) Comparison of methods for calculating stress intensity factors with quarter point elements. Int J Fract 32:127–140

    Article  Google Scholar 

  • Banks-Sills L, Sherman D (1992) On the computation of stress intensity factors for three-dimensional geometries by means of the stiffness derivative and J-integral methods. Int J Fract 53:1–20

    Google Scholar 

  • Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5):601–620

    Article  Google Scholar 

  • Bittencourt TN, Barry A, Ingraffea AR (1992) Comparison of mixed-mode stress intensity factors obtained through displacement correlation, J-integral formulation and modified crack-closure integral. In: Fracture mechanics: 22nd Symposium. Atluri SN, Newman,JC Jr, Raju IS, Epstein JS, editors, number II, ASTM STP, Philadelphia, pp 69-82

  • Bittencourt TN, Wawrzynek PA, Ingraffea AR, Sousa JL (1996) Quasi-automatic simulation of crack propagation for 2D LEFM problems. Eng Fract Mech 55(2):321–334

    Article  Google Scholar 

  • Bobet A, Einstein HH (1998) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92:221–252

    Article  Google Scholar 

  • Bourdin B, Francfort GA, Marigo JJ (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48:797–826

    Article  Google Scholar 

  • Clough RW (1960) The finite element method in plane stress analysis, Conference on matrix methods in structural mechanics, ASCE, Pittsburgh, PA: 345-378

  • Clough RW (1962) The stress distribution of Norfork Dam, structures and materials research. Department of civil engineering, University of California: Series 100, Issue 19, Berkeley

  • Duflot M (2007) A study of the representation of cracks with level sets. Int J Numer Methods Eng 70(11):1261–1302

    Article  Google Scholar 

  • Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46(8):1319–1342

    Article  Google Scholar 

  • Gallagher RH (1978) A review of finite element techniques in fracture mechanics. In: Proceedings of the first international conference on numerical methods in fracture mechanics (Luxmoore AR, Owen DRJ, Hrsg S) Swansea: Pineridge Press, pp 1–25

  • Gdoutos EE (1993) Fracture mechanics: an introduction. Solid mechanics and its applications. Kluwer Academic Publishers, Dordrecht, Holland

    Book  Google Scholar 

  • Giner E, Fuenmayor FJ, Baeza L, Tarancón JE (2005) Error estimation for the finite element evaluation of G\(_{{\rm I}}\) and G\(_{{\rm II}}\) in mixed-mode linear elastic fracture mechanics. Finite Elem Anal Des 41:1079–1104

    Article  Google Scholar 

  • Giner E, Sukumar N, Tarancón JE, Fuenmayor FJ (2009) An Abaqus implementation of the extended finite element method. Eng Fract Mech 76(3):347–368

    Article  Google Scholar 

  • Hansbo A, Hansbo P (2004) A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods Appl Mech Eng 19(33):3523–3540

    Article  Google Scholar 

  • Henshell RD, Shaw KG (1975) Crack tip elements are unnecessary. Int J Numer Methods Eng 9:495–507

    Article  Google Scholar 

  • Hibbitt, Karlsson, Sorensen (2004) Inc. ABAQUS/standard user’s manual, Pawtucket, Rhode Island

  • Ingraffea AR (2004) Computational fracture mechanics. In: Encyclopedia of computational mechanics, 1\(^{{\rm st}}\) edn. Wiley, pp 375-405

  • Jäger P, Steinmann P, Kuhl E (2008) Modelling three-dimensional crack propagation—a comparison of crack path tracking strategies. Int J Numer Methods Eng 76(9):1328–1352

    Article  Google Scholar 

  • Jirásek M (2011) Damage and smeared crack models. In: Hofstetter G, Meschke G (eds) Numerical modelling of concrete cracking. Springer, Berlin, pp 1–49

    Google Scholar 

  • Kanninen MF, Popelar CH (1985) Advanced fracture mechanics. Oxford University Press, Oxford (UK)

    Google Scholar 

  • Kuna M (2013) Finite elements in fracture mechanics. Theory—numerics—applications. Springer, Berlin

    Book  Google Scholar 

  • Marco M, Belda R, Miguélez MH, Giner E (2018a) A heterogeneous orientation criterion for crack modelling in cortical bone using a phantom-node approach. Finite Elem Anal Des 146:107–117

    Article  Google Scholar 

  • Marco M, Giner E, Larraínzar-Garijo R, Caeiro JR, Miguélez MH (2018b) Modelling of femur fracture using finite element procedures. Eng Fract Mech 196:157–167

    Article  Google Scholar 

  • Moës N, Gravouil A (2002) Non-planar 3D crack growth by the extended finite element method and level sets—part I: mechanical model. Int J Numer Methods Eng 53(11):2549–2568

    Article  Google Scholar 

  • Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150

    Article  Google Scholar 

  • Oliver J, Huespe AE, Samaniego E, Chaves EWV (2002) On strategies for tracking strong discontinuities in computational failure mechanics. In: Fifth world congress on computational mechanics. Mang HA, Rammerstorfer FC, Eberhardsteiner J. Vienna, Austria, pp 7-12

  • Ooi ET, Man H, Natarajan S, Song C (2015) Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling. Eng Fract Mech 144:101–117

    Article  Google Scholar 

  • Owen DRJ, Fawkes AJ (1983) Engineering fracture mechanics: numerical methods and applications. Pineridge Press Ltd., Swansea

    Google Scholar 

  • Qian G, Wang M (1996) Symmetric branching of mode II and mixed-mode fatigue crack growth in a stainless steel. J Eng Mater Technol 118:356–361

    Article  CAS  Google Scholar 

  • Qian G, González-Albuixech VF, Niffenegger M, Giner E (2016) Comparison of KI calculation methods. Eng Fract Mech 156:52–67

    Article  Google Scholar 

  • Rashid YR (1968) Analysis of prestressed concrete reactor vessels. Nucl Eng Des 7:334–334

    Article  Google Scholar 

  • Rice JR, Tracey DM (1973) Computational fracture mechanics. In: Numerical and computer methods in structural mechanics. Fenves SJ, Perrone N, Robinson AR, Schnobrich WC, Academic Press, New York, pp 585-623

  • Saouma VE, Ingraffea AR (1981) Fracture mechanics analysis of discrete cracking. In: Proceedings, IABSE colloquium on advanced mechanics of reinforced concrete, Delft 393

  • Song JH, Wang H, Belytschko T (2008) A comparative study on finite element methods for dynamic fracture. Comput Mech 42:239–250

    Article  Google Scholar 

  • Staroselsky A, Acharya R, Cassenti B (2019) Phase field modeling of fracture and crack growth. Eng Fract Mech 205:268–284

    Article  Google Scholar 

  • Stolarska D, Chopp L, Moës N, Belytschko T (2001) Modelling crack growth by level sets in the extended finite element method. Int J Numer Methods Eng 51(8):943–960

    Article  Google Scholar 

  • Turner MJ, Clough RW, Martin HC, Topp LJ (1956) Stiffness and deflection analysis of complex structures. J Aeronaut Sci 23:805–823

    Article  Google Scholar 

  • Xu X, Needleman A (1994) Numerical simulation of fast crack growth in brittle solids. J Mech Phys Solids 42(9):1397–1434

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the funding support received from the Spanish Ministerio de Ciencia, Innovación y Universidades and the FEDER operation program in the framework of the projects DPI2017-89197-C2-1-R and DPI2017-89197-C2-2-R and the FPI subprograms BES-2014-068473 and BES-2015-072070. The financial support of the Generalitat Valenciana through the Programme PROMETEO 2016/007 is also acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911, Leganés, Madrid, Spain

    Miguel Marco & Diego Infante-García

  2. Centre of Research in Mechanical Engineering–CIIM, Department of Mechanical and Materials Engineering, Universitat Politècnica de València, Camino de Vera, 46022, Valencia, Spain

    Ricardo Belda & Eugenio Giner

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  1. Miguel Marco
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  2. Diego Infante-García
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  3. Ricardo Belda
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  4. Eugenio Giner
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Correspondence to Miguel Marco.

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Marco, M., Infante-García, D., Belda, R. et al. A comparison between some fracture modelling approaches in 2D LEFM using finite elements. Int J Fract 223, 151–171 (2020). https://doi.org/10.1007/s10704-020-00426-6

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  • DOI: https://doi.org/10.1007/s10704-020-00426-6

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