Analysis of the delayed damage model for three one-dimensional loading scenarii

Jihed Zghal; Nicolas Moës

doi:10.5802/crphys.42

Analysis of the delayed damage model for three one-dimensional loading scenarii

Jihed Zghal ¹; Nicolas Moës ^2,³

¹ Laboratoire Energetique Mecanique Electromagnetisme (LEME), University of Paris Nanterre, 50 rue de sèvres 92410 Ville d’Avray, France
² Ecole Centrale de Nantes, GeM Institute, UMR CNRS 6183, 1 rue de la Noë, 44321 Nantes, France
³ Institut Universitaire de France (IUF), France

Comptes Rendus. Physique, Volume 21 (2020) no. 6, pp. 527-537.

Abstract
Résumé

The delayed damage model has been introduced by Allix and Deü [] as a way to overcome spurious mesh dependency in failure analysis involving damage and dynamic loading. The damage rate is bounded through a time scale which, combined with the wave speed, introduces implicitly a length scale. In this paper, the delayed damage model is analyzed through numerical experiments on three different loading cases of a bar: a slow loading leading to a dynamic failure, pulses and impact. We observe and discuss the load level needed for failure (and the dependence of this load level with respect to the loading rate), as well as the dissipation and extent of the fully damaged zone at failure. Observations lead to the following conclusions. First, the delayed damage model has no regularization effect for a dynamic failure initiating from rest. Second, for pulse loadings, the loading rate has no influence on the minimal load level needed for failure (even though the delayed damage model is a time-dependent model), and beyond this minimal load level for failure, the extent of the fully damage zone rises, proportionally to the length scale. Third, regarding the impact, the velocity needed to reach failure depends only the time-independent parameters of the models, and not the ones linked to the delayed damage.

Le modèle d’endommagement à effet retard a été introduit par Allix et Deü [] pour surmonter dans le cas de chargement dynamique la dépendance de maillage non-physique observée dans l’analyse de rupture. Le taux d’endommagement est limité via un temps caractéristique qui, combiné à la vitesse des ondes, introduit implicitement une longueur caractéristique. Dans cet article, le modèle d’endommagement à effet retard est analysé par des simulations numériques sur trois cas de chargement différents d’une barre : un chargement lent conduisant à une rupture dynamique, des impulsions et un impact. Nous observons et discutons le niveau de charge nécessaire à la rupture (et la dépendance de ce niveau de charge à la vitesse du chargement), ainsi que la dissipation et l’étendue de la zone entièrement endommagée lors de la rupture. Les observations conduisent aux conclusions suivantes. Premièrement, le modèle à effet retard n’a aucun effet de régularisation pour une défaillance dynamique démarrant du repos. Deuxièmement, pour les chargements par impulsions, la vitesse de chargement n’a aucune influence sur le niveau de charge minimal nécessaire à la rupture (alors que le modèle à effet retard est pourtant un modèle dépendant du temps), et au-delà de ce niveau de charge minimal pour la rupture, l’étendue du dommage total est proportionnelle à la longueur caractéristique. Troisièmement, en ce qui concerne l’impact, la vitesse nécessaire pour atteindre la rupture dépend uniquement des paramètres affectant la version indépendante du modèle (et non ceux liés à l’effet retard).

Published online: 2021-01-14

DOI: 10.5802/crphys.42

Keywords: Damage, Delay effect, Dynamics, Localization, Softening
Mot clés : Endommagement, Effet retard, Dynamique, Localisation, Adoucissement

Author's affiliations:

Jihed Zghal ¹; Nicolas Moës ^{2, 3}

¹ Laboratoire Energetique Mecanique Electromagnetisme (LEME), University of Paris Nanterre, 50 rue de sèvres 92410 Ville d’Avray, France
² Ecole Centrale de Nantes, GeM Institute, UMR CNRS 6183, 1 rue de la Noë, 44321 Nantes, France
³ Institut Universitaire de France (IUF), France

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

@article{CRPHYS_2020__21_6_527_0,
     author = {Jihed Zghal and Nicolas Mo\"es},
     title = {Analysis of the delayed damage model for three one-dimensional loading scenarii},
     journal = {Comptes Rendus. Physique},
     pages = {527--537},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {21},
     number = {6},
     year = {2020},
     doi = {10.5802/crphys.42},
     language = {en},
}

TY  - JOUR
AU  - Jihed Zghal
AU  - Nicolas Moës
TI  - Analysis of the delayed damage model for three one-dimensional loading scenarii
JO  - Comptes Rendus. Physique
PY  - 2020
SP  - 527
EP  - 537
VL  - 21
IS  - 6
PB  - Académie des sciences, Paris
DO  - 10.5802/crphys.42
LA  - en
ID  - CRPHYS_2020__21_6_527_0
ER  -

%0 Journal Article
%A Jihed Zghal
%A Nicolas Moës
%T Analysis of the delayed damage model for three one-dimensional loading scenarii
%J Comptes Rendus. Physique
%D 2020
%P 527-537
%V 21
%N 6
%I Académie des sciences, Paris
%R 10.5802/crphys.42
%G en
%F CRPHYS_2020__21_6_527_0

Jihed Zghal; Nicolas Moës. Analysis of the delayed damage model for three one-dimensional loading scenarii. Comptes Rendus. Physique, Volume 21 (2020) no. 6, pp. 527-537. doi : 10.5802/crphys.42. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.42/

References
Cited by

[1] O. Allix; J.-F. Deü Delayed-damage modelling for fracture prediction of laminated composites under dynamic loading, Eng. Trans., Volume 45 (1997) no. 1, pp. 29-46

[2] Z. P. Bazant; T. Belytschko Wave propagation in a strain-softening bar: exact solution, J. Eng. Mech., Volume 111 (1985), pp. 381-389

[3] G. Pijaudier-Cabot; Z. P. Bazant; M. Tabbara Comparison of various models for strain softening, Eng. Comput., Volume 5 (1988), pp. 141-150

[4] Z. P. Bazant; T. Belytschko; T.-P. Chang Continuum theory for strain-softening, J. Eng. Mech., Volume 110 (1984), pp. 1666-1692

[5] G. Pijaudier-Cabot; Z. P. Bazant Nonlocal dalmage theory, J. Eng. Mech. ASCE, Volume 113 (1987), pp. 1512-1533

[6] H. L. Schreyer; Z. Chen One-dimensional softening with localization, J. Appl. Mech., Volume 53 (1986), pp. 791-797

[7] N. Triantafyllidis; E. Aifantis A gradient approach to localization of deformation. I. Hyperelastic materials, J. Elast., Volume 16 (1986), pp. 225-237

[8] M. Frémond; B. Nedjar Damage, gradient of damage and principle of virtual power, Int. J. Solids Struct., Volume 33 (1996) no. 8, pp. 1083-1103

[9] R. Peerlings; R. De Borst; W. A. M. Brekelmans; J. Vree Gradient-enhanced damage for quasi-brittle materials, Int. J. Numer. Methods Eng., Volume 39 (1996), pp. 3391-3403

[10] G. Pijaudier-Cabot; N. Burlion Damage and localisation in elastic materials with voids, Mech. Cohesive Frict. Mater., Volume 144 (1996), pp. 129-144

[11] V. Hakim; A. Karma Laws of crack motion and phase-field models of fracture, J. Mech. Phys. Solids, Volume 57 (2009) no. 2, pp. 342-368

[12] B. Bourdin; G. a. Francfort; J.-J. Marigo The variational approach to fracture, J. Elast., Volume 91 (2008), pp. 5-148

[13] N. Moës; C. Stolz; P.-E. Bernard; N. Chevaugeon A level set based model for damage growth: the thick level set approach, Int. J. Numer. Methods Eng., Volume 86 (2011) no. 3, pp. 358-380

[14] R. Becker; A. Needleman; O. Richmond; V. Tvergaard Void growth and failure in notched bars, J. Mech. Phys. Solids, Volume 36 (1988) no. 3, pp. 317-351

[15] L. J. Sluys Wave propagation, localisation and dispersion in softening solids, Ph. D. Thesis, T.U. Delft (1992)

[16] J. C. Simo; J. W. Ju Strain- and stress-based continuum damage models. I. formulation, Int. J. Solids Struct., Volume 23 (1987), pp. 821-840

[17] J.-F. Dubé; G. Pijaudier-Cabot; C. L. Borderie Rate dependent damage model for concrete in dynamics, J. Eng. Mech., Volume 122 (1996) no. 10, pp. 939-947

[18] P. Perzyna Fundamental problems in viscoplasticity, Adv. Appl. Mech., Volume 9 (1966), pp. 243-377

[19] O. Allix; J. F. Deü; P. Ladevèze A delay damage meso-model for prediction of localisation and fracture of laminates subjected to high rates loading, Proceedings, European Conference on Computational Mechanics, München, Germany, Wiley, 1999

[20] T. von Karman On the propagation of plastic deformation in solids (1942) no. 0SRD 365, NDRC Report No A-29 (Technical report)

[21] T. Belytschko; L. Wing-Kam; K. Moran; B. Elkhodary Nonlinear Finite Elements for Continua and Structures, Wiley, UK, 2013

[22] A. Suffis; T. Lubrecht; A. Combescure Damage model with delay effect: Analytical and numerical studies of the evolution of the characteristic damage length, Int. J. Solids Struct., Volume 40 (2003) no. 13–14, pp. 3463-3476

[23] A. Suffis; A. Combescure Modèle d’endommagement à effet retard: Etude numérique et analytique de l’évolution de la longueur caractéristique, Revu. Euro. Eléments, Volume 11 (2002) no. 5, pp. 593-619

[24] T. Von Karman; P. Duwez The propagation of plastic deformation in solids, J. Appl. Phys., Volume 21 (1950) no. 10, pp. 987-994

Cited by Sources:

Comments - Policy