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A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM. (English) Zbl 1144.74043
Summary: We present a comparative study on finite elements for capturing strong discontinuities by means of elemental (E-FEM) or nodal enrichments (X-FEM). Based on the same constitutive model (continuum damage) and linear elements (triangles and tetrahedra), optimized implementations of both types of enrichments in the same nonlinear code are tested for a representative set of 2D and 3D crack propagation examples. It is shown that both methods provide the same qualitative and quantitative results for enough refined meshes. For the performed tests, E-FEM exhibited, in general, a higher accuracy, mostly for coarse meshes, whereas, convergence rate with mesh refinement, which is super-linear, showed slightly higher for X-FEM. As for the computational costs for single crack modelling X-FEM showed, depending on the case, from 1.1 to about 2.5 times more expensive than E-FEM. For multiple cracks, the computational cost of E-FEM keeps constant, whereas the cost associated to X-FEM increases linearly with the number of modelled cracks.

MSC:
74S05Finite element methods in solid mechanics
74R10Brittle fracture
Software:
XFEM
WorldCat.org
Full Text: DOI
References:
[1] Alfaiate, J.: New developments in the study of strong embedded discontinuities infinite elements. Adv. fract. Damage mech. 251 -- 252, 109-114 (2003)
[2] Armero, F.; Garikipati, K.: An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. Int. J. Solids struct. 33, 2863-2885 (1996) · Zbl 0924.73084
[3] Bazant, Z.; Cedolin, L.: Fracture mechanics of reinforced concrete. J. eng. Mech. div. ASCE, 1287-1305 (1980)
[4] Belytschko, T.; Chen, H.; Xu, J. X.; Zi, G.: Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int. J. Numer. methods engrg. 58, 1873-1905 (2003) · Zbl 1032.74662
[5] Belytschko, T.; Moes, N.; Usui, S.; Parimi, C.: Arbitrary discontinuities in finite elements. Int. J. Numer. methods engrg. 50, 993-1013 (2001) · Zbl 0981.74062
[6] C. Feist, G. Hofstetter, Computational aspects of concrete fracture simulations in the framework of the SDA. Presented at Fracture Mechanics of Concrete Structures FRAMCOS 2004, Vale, Co, USA, 2004.
[7] Garikipati, K.; Hughes, T. J. R.: A study of strain-localization in a multiple scale framework. The one dimensional problem. Comput. methods appl. Mech. engrg. 159, 193-222 (1998) · Zbl 0961.74009
[8] Gasser, T. C.; Holzapfel, G. A.: Geometrically non-linear and consistently linearized embedded strong discontinuity models for 3D problems with an application to the dissection analysis of soft biological tissues. Comput. methods appl. Mech. engrg. 192, 5059-5098 (2003) · Zbl 1088.74541
[9] Gasser, T. C.; Holzapfel, G. A.: Modeling 3D crack propagation in unreinforced concrete using PUFEM. Comput. methods appl. Mech. engrg. 194, 2859-2896 (2005) · Zbl 1176.74180
[10] Jirasek, M.: Comparative study on finite elements with embedded discontinuities. Comput. methods appl. Mech. engrg. 188, 307-330 (2000) · Zbl 1166.74427
[11] A.S. Kobayashi, M.N. Hawkins, D.B. Barker, B.M. Liaw, Fracture process zone of concrete, in: S.S.P. (Ed.), Application of Fracture Mechanics to Cementitious Composites, Marinus Nujhoff Publ., Dordrecht, 1985, pp. 25 -- 50.
[12] P. Laborde, J. Pommier, Y. Renard, M. Salaün, High order extended finite element method for cracked domains. Presented at Computational Plasticity VIII: Fundamentals and Applications, Barcelona, Spain, 2005. · Zbl 1181.74136
[13] Larsson, R.; Runesson, K.; Ottosen, N. S.: Discontinuous displacement approximation for capturing plastic localization. Int. J. Numer. methods engrg. 36, 2087-2105 (1993) · Zbl 0794.73074
[14] Liao, K.; Reifsnider, K. L.: A tensile strength model for unidirectional fiber-reinforced brittle matrix composite. Int. J. Fract. 106, 95-115 (2000)
[15] Cervera, M.; Agelet, C.; Chiumenti, M.: COMET: A multipurpose finite element code for numerical analysis in solid mechanics. (2001)
[16] Mariani, S.; Perego, U.: Extended finite element method for quasi-brittle fracture. Int. J. Numer. methods engrg. 58, 103-126 (2003) · Zbl 1032.74673
[17] N. Moës, N. Sukumar, B. Moran, T. Belytschko, An extended finite element method (X-FEM) for two and three-dimensional crack modelling. Presented at ECCOMAS 2000, Barcelona, Spain, 2000. · Zbl 0963.74067
[18] Mosler, J.; Meschke, G.: 3D modelling of strong discontinuities in elastoplastic solids: fixed and rotating localization formulations. Int. J. Numer. methods engrg. 57, 1553-1576 (2003) · Zbl 1062.74623
[19] Mosler, J.; Meschke, G.: Embedded crack vs. Smeared crack models: a comparison of elementwise discontinuous crack path approaches with emphasis on mesh bias. Comput. methods appl. Mech. engrg. 193, 3351-3375 (2004) · Zbl 1060.74606
[20] Oliver, J.: Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. 2. Numerical simulation. Int. J. Numer. methods engrg. 39, 3601-3623 (1996) · Zbl 0888.73018
[21] Oliver, J.: On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations. Int. J. Solids struct. 37, 7207-7229 (2000) · Zbl 0994.74004
[22] Oliver, J.; Huespe, A. E.: Continuum approach to material failure in strong discontinuity settings. Comput. methods appl. Mech. engrg. 193, 3195-3220 (2004) · Zbl 1060.74507
[23] Oliver, J.; Huespe, A. E.: Theoretical and computational issues in modelling material failure in strong discontinuity scenarios. Comput. methods appl. Mech. engrg. 193, 2987-3014 (2004) · Zbl 1067.74505
[24] J. Oliver, A.E. Huespe, S. Blanco, D.L. Linero, Stability and robustness issues in numerical modeling of material failure in the strong discontinuity approach, Comput. Methods Appl. Mech. Engrg. accepted for publication. · Zbl 05073260
[25] J. Oliver, A.E. Huespe, M.D.G. Pulido, S. Blanco, Recent advances in computational modelling of material failure. Presented at 4th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004), University of Jyväskylä, Jyväskylä, Finland, 2004.
[26] J. Oliver, A.E. Huespe, M.D.G. Pulido, S. Blanco, D. Linero, New developments in computational material failure mechanics. Presented at Sixth World Congress on Computational Mechanics (WCCM VI), Beijing, PR China, 2004.
[27] Oliver, J.; Huespe, A. E.; Pulido, M. D. G.; Chaves, E.: From continuum mechanics to fracture mechanics: the strong discontinuity approach. Engrg. fract. Mech. 69, 113-136 (2002)
[28] Oliver, J.; Huespe, A. E.; Samaniego, E.: A study on finite elements for capturing strong discontinuities. Int. J. Numer. methods engrg. 56, 2135-2161 (2003) · Zbl 1038.74645
[29] Borja, R. L.; Regueiro, R. A.: A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation. Comput. methods appl. Mech. engrg., 1529-1549 (2000) · Zbl 1003.74074
[30] Rots, J. G.: Computational modeling of concrete fractures. (1988)
[31] Runesson, K.; Mroz, Z.: A note on nonassociated plastic flow rules. Int. J. Plast. 5, 639-658 (1989) · Zbl 0697.73025
[32] Simo, J.; Oliver, J.; Armero, F.: An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. Comput. mech. 12, 277-296 (1993) · Zbl 0783.73024
[33] Simone, A.: Partition of unity-based discontinuous elements for interface phenomena: computational issues. Commun. numer. Methods engrg. 20, 465-478 (2004) · Zbl 1058.74082
[34] Spencer, B. W.; Shing, P. B.: Rigid-plastic interface for an embedded crack. Int. J. Numer. methods engrg. 56, 2163-2182 (2003) · Zbl 1038.74650
[35] Wells, G. N.; Sluys, L. J.: A new method for modelling cohesive cracks using finite elements. Int. J. Numer. methods engrg. 50, 2667-2682 (2001) · Zbl 1013.74074
[36] Willam, K.; Sobh, N.: Bifurcation analysis of tangential material operators. Transient/dynamic analysis and constitutive laws for engineering materials 2, C4/1-C4/13 (1987)
[37] Zi, G.; Belytschko, T.: New crack-tip elements for XFEM and applications to cohesive cracks. Int. J. Numer. methods engrg. 57, 2221-2240 (2003) · Zbl 1062.74633