Towards a generalization of a discrete strong discontinuity approach. (English) Zbl 1230.74177

Summary: A generalized discrete strong discontinuity approach (GSDA) is presented, in which non-homogeneous jumps are embedded in parent finite elements. The new formulation presents similar kinematics as for interface elements, accurately simulating both rigid body motion and stretching induced by the opening of a discontinuity. This generalized discrete strong discontinuity approach is built within the framework of strong embedded discontinuity formulations; as a consequence, it is mesh independent and avoids the progressive remeshing needed with interface elements. The GSDA can be viewed as a generalization of other embedded formulations for which particular assumptions are adopted regarding both the jump transmission and the variational principle.
Structural examples including mode-I, mode-II and mixed-mode fracture are computed and compared with other embedded formulations and experimental results.


74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
Full Text: DOI


[1] Hillerborg, A.; Modeer, M.; Petersson, P.E., Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cem. concr. res., 6, 6, 773-781, (1976)
[2] M. Arrea, A. Ingraffea, Mixed Mode Crack Propagation in Mortar and Concrete, Technical Report 81-13, Department of Structural Engineering, Cornell University, USA, 1982.
[3] Ingraffea, A.; Saouma, V., Numerical modelling of discrete crack propagation in reinforced and plain concrete, ()
[4] Bocca, P.; Carpinteri, A.; Valente, S., Mixed mode fracture of concrete, International journal of solids and structures, 27, 1139-1153, (1986)
[5] J. Alfaiate, E.B. Pires, J.A.C. Martins, A finite element model for the study of crack propagation, in: M.H. Aliabadi, D.J. Cartwright, H.Nisitani (Eds.), Proceedings of the Second International Conference on Localised Damage, Computational Mechanics Publications and Elsevier Applied Science, Southampton, United Kingdom, 1992, pp. 261-282.
[6] Alfaiate, J.; Pires, E.B.; Martins, J.A.C., A finite element analysis of non-prescribed crack propagation in concrete, Comput. struct., 63, 1, 17-26, (1997) · Zbl 0899.73512
[7] Ortiz, M.; Leroy, Y.; Needleman, A., A finite element method for localized failure analysis, Comput. methods appl. mech. engrg., 61, 2, 189-214, (1987) · Zbl 0597.73105
[8] Sluys, L.J.; Berends, A.H., Discontinuous failure analysis for mode-I and mode-II localization problems, Int. J. solids struct., 35, 31-32, 4257-4274, (1998) · Zbl 0933.74060
[9] Dvorkin, E.N.; Cuitiño, A.M.; Gioia, G., Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions, Int. J. numer. methods engrg., 30, 3, 541-564, (1990) · Zbl 0729.73209
[10] Simo, J.C.; 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
[11] Oliver, J.; Cervera, M.; Manzoli, O., Strong discontinuities and continuum plasticity models: the strong discontinuity approach, Int. J. plast., 15, 3, 319-351, (1999) · Zbl 1057.74512
[12] Oliver, J.; Huespe, A.E., A study on finite elements for capturing strong discontinuities, Int. J. numer. methods engrg., 56, 2135-2161, (2003) · Zbl 1038.74645
[13] Oliver, J.; Huespe, A.E.; Samaniego, E.; Chaves, E.W.V., Continuum approach to the numerical simulation of material failure in concrete, Int. J. numer. anal. meth. geomech., 28, 609-632, (2004) · Zbl 1112.74493
[14] Jirásek, M., Comparative study on finite elements with embedded discontinuities, Comput. methods appl. mech. engrg., 188, 1-3, 307-330, (2000) · Zbl 1166.74427
[15] Larsson, R.; Runesson, K.; Sture, S., Embedded localization band in undrained soil based on regularized strong discontinuity – theory and fe-analysis, Int. J. solids struct., 33, 20-22, 3081-3101, (1996) · Zbl 0919.73279
[16] Larsson, R.; Runesson, K., Element-embedded localization band based on regularized displacement discontinuity, J. engrg. mech., 122, 5, 402-411, (1996)
[17] Lofti, H.R.; Shing, P.B., Embedded representation of fracture in concrete with mixed finite elements, Int. J. numer. methods engrg., 38, 8, 1307-1325, (1995) · Zbl 0824.73070
[18] Klisinski, M.; Runesson, K.; Sture, S., Finite element with inner softening band, J. engrg. mech., 117, 3, 575-587, (1991)
[19] 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, 20-22, 2863-2885, (1996) · Zbl 0924.73084
[20] Oliver, J., Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. part 1: fundamentals, Int. J. numer. methods engrg., 39, 21, 3575-3600, (1996) · Zbl 0888.73018
[21] Oliver, J., Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. part 2: numerical simulation, Int. J. numer. methods engrg., 39, 21, 3601-3623, (1996) · Zbl 0888.73018
[22] Jirásek, M.; Zimmermann, T., Embedded crack model: I. basic formulation, Int. J. numer. methods engrg., 50, 6, 1269-1290, (2001) · Zbl 1013.74068
[23] Bolzon, G., Formulation of a triangular finite element with an embedded interface via isoparametric mapping, Comput. mech., 27, 463-473, (2001) · Zbl 1052.74053
[24] Alfaiate, J.; Simone, A.; Sluys, L.J., Non-homogeneous displacement jumps in strong embedded discontinuities, Int. J. solids struct., 40, 21, 5799-5817, (2003) · Zbl 1059.74548
[25] Linder, C.; Armero, F., Finite elements with embedded strong discontinuities for the modeling of failure in solids, Int. J. numer. methods engrg., 72, 12, 1391-1433, (2007) · Zbl 1194.74431
[26] Oliver, J.; Linero, D.L.; Huespe, A.E.; Manzoli, O.L., Two-dimensional modeling of material failure in reinforced concrete by means of a continuum strong discontinuity approach, Comput. methods appl. mech. engrg., 197, 5, 332-348, (2008) · Zbl 1169.74566
[27] D. Dias-da-Costa, J. Alfaiate, L.J. Sluys, E. Júlio, A discrete strong discontinuity approach, Eng. Fract. Mech. doi: 10.1016/j.engfracmech.2009.01.011. · Zbl 1230.74177
[28] Ohlsson, U.; Olofsson, T., Mixed-mode fracture and anchor bolts in concrete analysis with inner softening bands, J. engrg. mech., 123, 10, 1027-1033, (1997)
[29] J.Alfaiate, L.J. Sluys, On the use of embedded discontinuities in the framework of a discrete crack approach, in: W.Z.Z. Yao, M. Yuan (Ed.), Proceedings of the Sixth International Congress on Computational Mechanics in Conjunction with the Second Asian-Pacific Congress of Computational Mechanics, WCCMVI, Beijing, China, 2004.
[30] J.J.C. Remmers, Discontinuities in Materials and Structures: A Unifying Computational Approach, Ph.D. Thesis, Delft University of Technology, 2006.
[31] Malvern, L.E., Introduction to the mechanics of a continuous medium, (1969), Prentice-Hall International Englewood Cliffs, New Jersey · Zbl 0181.53303
[32] Alfaiate, J.; Wells, G.N.; Sluys, L.J., On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture, Engrg. fract. mech., 69, 6, 661-686, (2002)
[33] Washizu, K., Variational methods in elasticity and plasticity, (1982), Pergamon Press Ltd. Oxford · Zbl 0164.26001
[34] J. Alfaiate, Estudo e modelação do comportamento do betão fissurado, Ph.D. Thesis, Universidade Técnica de Lisboa, Instituto Superior Técnico, 1992.
[35] Alfaiate, J.; Pires, E.B., Evolução da fissuração num túnel de betão, Revista internacional de Métodos numéricos para Cálculo y diseño en ingeniería, 17, 185-197, (2001) · Zbl 0978.74534
[36] Coutinho, A.L.G.A.; Martins, M.A.D.; Sydenstricker, R.M.; Alves, J.L.D.; Landau, L., Simple zero thickness kinematically consistent interface elements, Comput. geotech., 30, 5, 347-374, (2003)
[37] Kaliakin, V.N.; Li, J., Insight into deficiencies associated with commonly used zero-thickness interface elements, Comput. geotech., 17, 2, 225-252, (1995)
[38] Schellekens, J.C.J.; DeBorst, R., On the numerical integration of interface elements, Int. J. numer. methods engrg., 36, 1, 43-66, (1993) · Zbl 0825.73840
[39] Simone, A., Partition of unity-based discontinuous elements for interface phenomena: computational issues, Commun. numer. methods engrg., 20, 6, 465-478, (2004) · Zbl 1058.74082
[40] D. Dias-da-Costa, J. Alfaiate, E. Júlio, Modelação numérica de descontinuidades fortes baseada numa abordagem de fenda discreta, in: APMTAC (Ed.), CMNE CILAMCE, Porto, Portugal, 2007, pp. 1-18.
[41] Manzoli, O.L.; Shing, P.B., A general technique to embed non-uniform discontinuities into standard solid finite elements, Comput. struct., 84, 10-11, 742-757, (2006)
[42] Galvez, J.C.; Elices, M.; Guinea, G.V.; Planas, J., Mixed mode fracture of concrete under proportional and nonproportional loading, Int. J. fract., 94, 3, 267-284, (1998)
[43] Galvez, J.C.; Cervenka, J.; Cendon, D.A.; Saouma, V., A discrete crack approach to normal/shear cracking of concrete, Cem. concr. res., 32, 10, 1567-1585, (2002)
[44] E. Schlangen, Experimental and Numerical Analysis of Fracture Processes in Concrete, Ph.D. Thesis, Delft University of Technology, 1993.
[45] M.B. Nooru-Mohamed, Mixed-mode Fracture of Concrete: An Experimental Approach, Ph.D. Thesis, Delft University of Technology, 1992.
[46] Cervera, M.; Chiumenti, M., Smeared crack approach: back to the original track, Int. J. numer. anal. methods geomech., 30, 12, 1173-1199, (2006) · Zbl 1196.74180
[47] Pivonka, P.; Ozbolt, J.; Lackner, R.; Mang, H.A., Comparative studies of 3d-constitutive models for concrete: application to mixed-mode fracture, Int. J. numer. methods engrg., 60, 2, 549-570, (2004) · Zbl 1098.74674
[48] Gasser, T.C.; Holzapfel, G.A., 3D crack propagation in unreinforced concrete: a two-step algorithm for tracking 3d crack paths, Comput. methods appl. mech. engrg., 195, 37-40, 5198-5219, (2006) · Zbl 1154.74376
[49] Feist, C.; Hofstetter, G., An embedded strong discontinuity model for cracking of plain concrete, Comput. methods appl. mech. engrg., 195, 52, 7115-7138, (2006) · Zbl 1331.74164
[50] J. Alfaiate, L. Sluys, Discontinuous numerical modelling of fracture using embedded discontinuities, in: D.R.J. Owen, E.O. Nate, B. Suárez (Eds.), Computational Plasticity Fundamentals and Applications, COMPLAS VIII, Barcelona, Spain, 2005.
[51] Babuška, I.; Melenk, J.M., The partition of unity method, Int. J. numer. methods engrg., 40, 4, 727-758, (1997) · Zbl 0949.65117
[52] Duarte, C.A.M.; Babuška, I.; Oden, J.T., Generalized finite element methods for three-dimensional structural mechanics problems, Comput. struct., 77, 2, 215-232, (2000)
[53] D. Dias-da Costa, J. Alfaiate, L.J. Sluys, E. Júlio, A comparative study on numerical modelling of discrete fracture of quasi-brittle materials using strong discontinuities, in: Proceedings of APCOM’07 in Conjunction with EPMESC XI, Kyoto, Japan, 2007.
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