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Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach. (English) Zbl 1331.74168
Summary: Robustness and stability of the Continuum Strong Discontinuity Approach (CSDA) to material failure are addressed. After identification of lack of symmetry of the finite element formulation and material softening in the constitutive model as possible causes of loss of robustness, two remedies are proposed: (1) the use of an specific symmetric version of the elementary enriched (E-FEM) finite element with embedded discontinuities and (2) a new implicit–explicit integration of the internal variable, in the constitutive model, which renders the tangent constitutive algorithmic operator positive definite and constant. The combination of both developments leads to finite element formulations with constant, in the time step, and non-singular tangent structural stiffness, allowing dramatic improvements in terms of robustness and computational costs. After assessing the convergence and stability properties of the new strategies, three-dimensional numerical simulations of failure problems illustrate the performance of the proposed procedures.

74S05 Finite element methods applied to problems in solid mechanics
74R99 Fracture and damage
74E30 Composite and mixture properties
Full Text: DOI
[1] Alfaiate, J., New developments in the study of strong embedded discontinuities in finite elements, Adv. fract. damage mech., 251-2, 109-114, (2003)
[2] Alfaiate, J.; Simone, A.; Sluys, L.J., Non-homogeneous displacement jumps in strong embedded discontinuities, Int. J. solids struct., 40, 5799-5817, (2003) · Zbl 1059.74548
[3] Armero, F.; Garikipati, K., Recent advances in the analysis and numerical simulation of strain localization in inelastic solids, Presented at computational plasticity. fundamentals and applications, (1995) · Zbl 0924.73084
[4] 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
[5] Arrea, M.; Ingraffea, A.R., Mixed-mode crack propagation in mortar and concrete, (1982), Dept. Struct. Eng. cornell Univ. New York, pp. 81-13
[6] Belytschko, T.; Möes, N.; Usui, S.; Parimi, C., Arbitrary discontinuities in finite elements, Int. J. numer. methods engrg., 50, 993-1013, (2001) · Zbl 0981.74062
[7] Bocca, P.; Carpintieri, A.; Valente, S., Size effect in the mixed mode crack propagation: softening and snap-back analysis, Engrg. fract. mech., 35, 159-170, (1990)
[8] Bolzon, G.; Corigliano, A., A discrete formulation for elastic solids with damaging interfaces, Comput. methods appl. mech. engrg., 140, 329-359, (1997) · Zbl 0891.73053
[9] Bolzon, G.; Corigliano, A., Finite elements with embedded displacement discontinuity: a generalized variable formulation, Int. J. numer. methods engrg., 49, 1227-1266, (2000) · Zbl 1004.74067
[10] C.C. Celigoj, On strong discontinuities in anelastic solids, A finite element approach taking a frame indifferent gradient of the discontinuous displacements, Presented at Int. J. Numer. Meth. Engng., 2000. · Zbl 1009.74061
[11] de Borst, R.; Wells, G.N.; Sluys, L.J., Some observations on embedded discontinuity models, Engrg. comput., 18, 241-254, (2001) · Zbl 0997.74061
[12] Dvorkin, E.N.; Cuitino, A.M.; Gioia, G., Finite elements with displacement embedded localization lines insensitive to mesh size and distortions, Int. J. numer. methods engrg., 30, 541-564, (1990) · Zbl 0729.73209
[13] R. Eligehausen, J. Ozbolt, Size effect in design of fastenings, in Mechanics of quasi-brittle materials and structures a volume in honour of prof. Zdenek P. Bazant 60th birthday: Gilles Pijaudier-Cabot, Zdenek Bittnar, Bruno Gérard, Paris Editions Hermes, 1999, pp. 95-118.
[14] R.B.P.C.V. Eligehausen, R. Pukl, Size effect of the concrete cone failure load of anchor bolts, Presented at Framcos-1, 1992.
[15] G.V. Guinea, M. Elices, J. Planas, Measuring the tensile strength through size effect curves, Presented at Fracture Mechanics of Concrete Strucutres, Framcos-3, Gifu, Japan, 1998.
[16] Jirasek, M., Comparative study on finite elements with embedded discontinuities, Comput. methods appl. mech. engrg., 188, 307-330, (2000) · Zbl 1166.74427
[17] 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
[18] Lofti, H.R.; Shing, P.B., Embedded representation of fracture in concrete with mixed finite-elements, Int. J. numer. methods engrg., 38, 1307-1325, (1995) · Zbl 0824.73070
[19] 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.
[20] NW-IALAD. Integrity Assessment of large concrete dams, European Research Network. Available from: <http://nw-ialad.uibk.ac.at/Wp2/Tg3/Se5/Ss9/>.
[21] Oliver, J., A consistent characteristic length for smeared cracking models, Int. J. numer. methods engrg., 28, 461-474, (1989) · Zbl 0676.73066
[22] Oliver, J., Continuum modelling of strong discontinuities in solid mechanics using damage models, Comput. mech., 17, 49-61, (1995) · Zbl 0840.73051
[23] Oliver, J., Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. 1 fundamentals, Int. J. numer. methods engrg., 39, 3575-3600, (1996) · Zbl 0888.73018
[24] 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
[25] 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
[26] Oliver, J., Topics on failure mechanics, International center for numerical methods in engineering (CIMNE) monograph no. 68, (2002) · Zbl 1137.74005
[27] Oliver, J.; Cervera, M.; Manzoli, O., Strong discontinuities and continuum plasticity models: the strong discontinuity approach, Int. J. plast., 15, 319-351, (1999) · Zbl 1057.74512
[28] 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
[29] 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
[30] 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)
[31] Oliver, J.; Huespe, A.E.; Pulido, M.D.G.; Samaniego, E., On the strong discontinuity approach in finite deformation settings, Int. J. numer. methods engrg., 56, 1051-1082, (2003) · Zbl 1031.74010
[32] 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
[33] 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. methods geomech., 28, 609-632, (2004) · Zbl 1112.74493
[34] J. Oliver, A.E. Huespe, P.J. Sánchez, A comparative study on finite elements with embedded discontinuities: E-FEM vs. X-FEM, Comput. Methods Appl. Mech. Engrg., in press. · Zbl 1144.74043
[35] 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
[36] Regueiro, R.A.; Borja, R.I., Plane strain finite element analysis of presure sensitive plasticity with strong discontinuity, Int. J. solids struct., 3647-3672, (2001) · Zbl 1031.74013
[37] J.G. Rots, Computational Modeling of Concrete Fractures, Delft University of Technology, 1988.
[38] Rots, J.G., Sequentially linear continuum model for concrete fracture, (), 831-839
[39] Rots, J.G.; Invernizzi, S., Regularized saw-tooth softening, (), 599-617 · Zbl 1112.74476
[40] J. Simo, J. Oliver, A new approach to the analysis and simulation of strong discontinuities, presented at Fracture and Damage in Quasi-brittle Structures, 1994.
[41] 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
[42] Simo, J.C.; Hughes, T.J.R., Computational inelasticity, (1998), Springer · Zbl 0934.74003
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