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Continuum approach to material failure in strong discontinuity settings. (English) Zbl 1060.74507
Summary: The paper focuses the numerical modelling of material failure in a strong discontinuity setting using a continuum format. Displacement discontinuities, like fractures, cracks, slip lines, etc., are modelled in a strong discontinuity approach, enriched by a transition from weak to strong discontinuities to get an appropriate representation of the fracture process zone. The introduction of the strong discontinuity kinematics automatically projects any standard dissipative constitutive model, equipped with strain softening, into a discrete traction-separation law that is fulfilled at the discontinuity interface. Numerical issues like a global discontinuity tracking algorithm via a heat conduction-like problem are also presented. Some representative numerical simulations illustrate the performance of the presented approach.

MSC:
74A45 Theories of fracture and damage
Software:
COMET
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[1] 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
[2] Bazant, Z.P., Crack band theory for fracture of concrete, Mater. construct., 93, 155-177, (1983)
[3] Bazant, Z.P.; Planas, J., Fracture and size effect in concrete and other quasibrittle materials, (1998), CRC Press Boca Raton, FL
[4] Belytschko, T.; Moës, N.; Usui, S.; Parimi, C., Arbitrary discontinuities in finite elements, Int. J. numer. methods engrg., 50, 993-1013, (2001) · Zbl 0981.74062
[5] 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)
[6] M. Cervera, C. Agelet de Saracibar, M. Chiumenti, COMET: a multipurpose finite element code for numerical analysis in solid mechanics. Technical Report, Technical University of Catalonia (UPC), 2001 · Zbl 1210.74170
[7] de Borst, R.; Sluys, L.J.; Muhlhaus, H.B.; Pamin, J., Fundamental issues in finite element analyses of localization of deformation, Engrg. comput., 10, 99-121, (1993)
[8] Diez, P.; Arroyo, M.; Huerta, A., Adaptivity based on error estimation for viscoplastic softening materials, Mech. cohes.-frict. mater., 5, 87-112, (2000)
[9] Dvorkin, E.N.; Cuitino, A.M.; Gioia, G., Finite elements with displacement embedded localization lines insensitive to mesh size and distortions, Int. J. numer. meth. engrg., 30, 541-564, (1990) · Zbl 0729.73209
[10] Faria, R.; Oliver, J.; Cervera, M., A strain-based plastic viscous-damage model for massive concrete structures, Int. J. solids struct., 14, 1533-1558, (1998) · Zbl 0920.73326
[11] Hillerborg, A., The theoretical basis of a method to determine the fracture energy gf of concrete, Mater. construct., 18, 106, 291-296, (1985)
[12] Lemaitre, J., A continuous damage mechanics model for ductile fracture, J. engrg. mater. technol., trans. ASME, 107, 83-89, (1985)
[13] Lofti, H.R.; Benson Shing, P., Embedded representation of fracture in concrete with mixed finite elements, Int. J. numer. methods engrg., 38, 1307-1325, (1995) · Zbl 0824.73070
[14] Lubliner, J., Plasticity theory, (1990), Mcmillan Publishing Company New York · Zbl 0745.73006
[15] N. Moës, N. Sukumar, B. Moran, Belytschko T. An extended finite element method (X-FEM) for two and three-dimensional crack modelling. In ECCOMAS 2000, Barcelona, Spain, September 11-14, 2000. Vienna University of Technology, Austria, ISBN 3-9501554-0-6
[16] Needleman, A.; Tvergard, V., Analysis of plastic localization in metals, Appl. mech. rev., 3-18, (1992)
[17] Oliver, J., Continuum modelling of strong discontinuities in solid mechanics using damage models, Comput. mech., 17, l-2, 49-61, (1995) · Zbl 0840.73051
[18] Oliver, J., Modeling 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
[19] 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
[20] 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
[21] Oliver, J.; Huespe, A.; Pulido, M.D.G.; Chaves, E., From continuum mechanics to fracture mechanics: the strong discontinuity approach, Engrg. fract. mech., 69, 2, 113-136, (2002)
[22] Oliver, J.; Huespe, A.; Samaniego, E., A study on finite elements for capturing strong discontinuities, Int. J. numer. meth. engrg., 56, 2135-2161, (2003) · Zbl 1038.74645
[23] J. Oliver, A.E. Huespe, Theoretical and computational issues in modeling material failure in strong discontinuity scenarios, Comput. Methods Appl. Mech. Engrg., in press · Zbl 1067.74505
[24] Oliver, J.; Huespe, A.E.; Pulido, M.D.G.; Samaniego, E., On the strong discontinuity approach in finite deformation settings, Int. J. numer. meth. engrg., 56, 1051-1082, (2003) · Zbl 1031.74010
[25] J. Oliver, A.E. Huespe, E. Samaniego, E.W.V. Chaves, On strategies for tracking strong discontinuities in computational failure mechanics. In: H.A. Mang, F.G. Rammer-storfer, J. Eberhardsteiner, (Eds.), Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), Swansea, July 7-12, 2002, Vienna University of Technology, Austria, ISBN 3-9501554-0-6, Available from <http://wccm.tuwien.ac.at>
[26] Rots, J.G.; Nauta, P.; Kusters, G.M.A.; Blaauwendraad, J., Smeared crack approach and fracture localization in concrete, Heron, 30, l, 1-49, (1985)
[27] Runesson, K.; Ottosen, N.S.; Peric, D., Discontinuous bifurcations of elastic-plastic solutions at plane stress and plane strain, Int. J. plast., 7, 99-121, (1991) · Zbl 0761.73035
[28] Simo, J.; Oliver, J., A new approach to the analysis and simulation of strong discontinuities, (), 25-39
[29] Simo, J.; Oliver, J.; Armero, F., An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, Computat. mech., 12, 277-296, (1993) · Zbl 0783.73024
[30] Simo, J.C.; Hughes, T.J.R., Computational inelasticity, (1998), Springer Berlin · Zbl 0934.74003
[31] Simo, J.C.; Ju, J.W., Stress and strain based continuum damage models: I formulation, Int. J. solids struct., 15, 821-840, (1987) · Zbl 0634.73106
[32] Stein, E.; Steinmann, P.; Miehe, C., Instability phenomena in plasticity: modelling and computation, Computat. mech., 17, 74-87, (1995) · Zbl 0860.73017
[33] 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
[34] Willam, K., Constitutive models for engineering materials, (), 603-633
[35] Zienkiewicz, O.C.; Taylor, R.L., The finite element method, (2000), Butterworth-Heinemann Oxford, UK · Zbl 0991.74002
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