Modélisation « macro » de phénomènes dissipatifs localisés à l’échelle « micro »
Formulation et implantation numérique
Keywords:
strain localization, fracture, strong discontinuities, finite element methodsAbstract
In this paper, we present a model capable of taking into account both diffuse dissipative mechanisms taking place at the structure scale and localized dissipative mechanisms taking place at finer scale: the localization zones. This is achieved by introducing in a continuum domain discontinuities of the displacement field. The method proposed herein is capable of combining two types of dissipation: a volumic one taken into account by a classical continuum model and a surfacic one taken into account by the introduction of discrete type laws.
Downloads
References
[ASA 83] ASARO R., « Micromechanics of crystals and polycrystals », Advanced in Applied
Mechanics, vol. 23, 1983, p. 1-115.
[BAŽ 84] BAŽANT Z.P., BELYTSCHKO T., CHANG T.P., « Continuum Theory for Strain
Softening », Journal of Engineering Mechanics, vol. 110, no 12, 1984, p. 1666-1691.
[BEL 99] BELYTSCHKO T., BLACK T., « Elastic Crack Growth in Finite Elements With Minimal
Remeshing », International Journal for Numerical Methods in Engineering, vol. 45,
no 5, 1999, p. 601-620.
[BOR 92] DE BORST R., MUHLHAUS H.B., PAMIN J., SLUYS L.J., « Computational Modelling
of Localisation of Deformation », Computational Plasticity III, Owen and Onate eds,
, p. 483-502.
[HUG 79] HUGHES T.J.R., « Generalization of selective integration procedures to anisotropic
and nonlinear media », International Journal for Numerical Methods in Engineering,
vol. 15, no 9, 1979, p. 1413-1418.
[HUG 87] HUGHES T.J.R., The Finite Element Methods, Prentice-Hall, Englewood-Cliffs,
N.J., 1987.
[IBR 91] IBRAHIMBEGOVI´C A., WILSON E.L., « A modified method of incompatible
modes », Communications in Applied Numerical Methods, vol. 7, 1991, p. 187-194.
[IBR 03] IBRAHIMBEGOVI´C A., BRANCHERIE D., « Combined hardening and softening
constitutive model of plasticity : precursor to shear slip line failure », Computational Mechanics,
vol. 31, 2003, p. 88-100.
[JIR 01] JIRÁSEK M., ZIMMERMANN T., « Embedded crack model : II. Combination with
smeared cracks », International Journal for Numerical Methods in Engineering, vol. 50,
, p. 1291-1305.
[MAZ 84] MAZARS J., « Application de la mécanique de l’endommagment au comportement
non linéaire du béton de structure », Thèse de doctorat, Thèse de doctorat de l’université de
Paris 6, 1984.
[MEL 96] MELENK J.M., BABUŠKA I., « The partition of unity finite element method : Basic
theory and applications », Computer Methods in Applied Mechanics and Engineering,
vol. 136, 1996, p. 289-314.
[NEE 88] NEEDLEMAN A., « Material Rate Dependence and Mesh Sensitivity in Localization
Problems », Computer Methods in Applied Mechanics and Engineering, vol. 63, 1988,
p. 69-85.
[PIJ 87] PIJAUDIER-CABOT G., BAŽANT ., « Nonlocal damage theory », ASCE Journal of
Engineering Mechanics, vol. 113, 1987, p. 1512-1533.
[WEL 01] WELLS G.N., SLUYS L.J., « A new method for modelling cohesive cracks using
finite elements », International Journal for Numerical Methods in Engineering, vol. 50,
, p. 2667-2682.
[WIL 73] WILSON E.L., TAYLOR R.L., DOHERTY W.P., GHABOUSSI J., « Incompatible
displacement models », FENVES S., AL., Eds., Numerical and Computer Methods in
Structural Mechanics, p. 43-57, Academic Press, 1973.
[WIL 90] WILSON E.L., IBRAHIMBEGOVI´C A., « Use of incompatible displacement modes
for the calculation of element stiffnesses or stresses », Finite Elements in Analysis and
Design, vol. 7, 1990, p. 229-241.