Local Continuum Damage Mechanics models cannot represent the entire degradation process in materials exhibiting strain-softening behaviors. It is well known that the rate equilibrium problem becomes ill-posed when softening occurs, and an infinity of solutions exists. From a numerical point of view, finite element analyses suffer from mesh-dependent results. Non-local models are generally used to regularize the structural response and recover objectivity. However, some physical inconsistencies can be observed in numerical results, e.g., damage diffusion over large damaged bands and damage attraction on the boundary of the computational domain. Non-local formulations with evolving interactions may better describe the damaging process and overcome these issues. This paper uses the so-called spalling test to underline the main drawbacks and advantages of several regularized models with constant and evolving non-local interactions. Concerning non-local formulations with constant interactions, attention is focused on the integral non-local formulation on the internal variable of the constitutive model and an implicit gradient damage formulation. Regarding formulations with evolving non-local interactions, attention is focused on a “stress-based integral non-local” approach and the so-called “eikonal non-local” approach. In this latter case, both its integral-type and gradient-type variants are considered.
Les modèles d’endommagement classiques ne sont pas capables de représenter l’ensemble du processus de dégradation ayant lieu pendant l’adoucissement en déformation. Dans le cadre de la méthode des éléments finis, des résultats dépendants du maillage sont obtenus. Des modèles non-locaux sont généralement utilisés pour régulariser la réponse structurelle et retrouver l’objectivité vis-à-vis du maillage. Cependant, certaines incohérences physiques peuvent être observées, telles que la diffusion progressive de l’endommagement et son attraction par la frontière du domaine. Les approches non-locales avec interactions évolutives peuvent mieux décrire le processus de fissuration et surmonter ces problèmes. Dans cet article, le test d’écaillage est utilisé pour souligner certains inconvénients et avantages typiques de différentes méthodes de régularisation. En particulier, l’attention est portée sur la formulation intégrale non-locale sur la variable interne du modèle de comportement, sur une formulation à gradient implicite, sur une approche intégrale non-locale basée sur les contraintes et sur l’approche non-locale dite eikonale. Dans ce dernier cas, ses formulations intégrales et de type gradient sont considérées.
Revised:
Accepted:
Published online:
Mot clés : Endommagement, Régularisation non-locale, Écaillage, Bords, Diffusion de l’endommagement
Breno Ribeiro Nogueira 1, 2; Cédric Giry 1; Giuseppe Rastiello 3; Fabrice Gatuingt 1
CC-BY 4.0
@article{CRMECA_2022__350_G3_507_0,
author = {Breno Ribeiro Nogueira and C\'edric Giry and Giuseppe Rastiello and Fabrice Gatuingt},
title = {One-dimensional study of boundary effects and damage diffusion for regularized damage models},
journal = {Comptes Rendus. M\'ecanique},
pages = {507--546},
publisher = {Acad\'emie des sciences, Paris},
volume = {350},
year = {2022},
doi = {10.5802/crmeca.137},
language = {en},
}
TY - JOUR AU - Breno Ribeiro Nogueira AU - Cédric Giry AU - Giuseppe Rastiello AU - Fabrice Gatuingt TI - One-dimensional study of boundary effects and damage diffusion for regularized damage models JO - Comptes Rendus. Mécanique PY - 2022 SP - 507 EP - 546 VL - 350 PB - Académie des sciences, Paris DO - 10.5802/crmeca.137 LA - en ID - CRMECA_2022__350_G3_507_0 ER -
%0 Journal Article %A Breno Ribeiro Nogueira %A Cédric Giry %A Giuseppe Rastiello %A Fabrice Gatuingt %T One-dimensional study of boundary effects and damage diffusion for regularized damage models %J Comptes Rendus. Mécanique %D 2022 %P 507-546 %V 350 %I Académie des sciences, Paris %R 10.5802/crmeca.137 %G en %F CRMECA_2022__350_G3_507_0
Breno Ribeiro Nogueira; Cédric Giry; Giuseppe Rastiello; Fabrice Gatuingt. One-dimensional study of boundary effects and damage diffusion for regularized damage models. Comptes Rendus. Mécanique, Volume 350 (2022), pp. 507-546. doi : 10.5802/crmeca.137. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.137/
[1] Nonlocal damage theory, J. Eng. Mech., Volume 113 (1987) no. 10, pp. 1512-1533
[2] Bifurcation and localization in rate-independent materials. Some general considerations, Bifurcation and Stability of Dissipative Systems, Springer, Vienna, 1993, pp. 1-44
[3] Strain softening of rock, soil and concrete—A review article, Mech. Mater., Volume 3 (1984) no. 4, pp. 271-294 | DOI
[4] Localization analysis of elastic degradation with application to scalar damage, J. Eng. Mech., Volume 121 (1995) no. 4, pp. 541-554
[5] Enhanced damage modelling for fracture and fatigue, Ph. D. Thesis, Technische Universiteit Eindhoven (1999)
[6] Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cem. Concr. Res., Volume 6 (1976) no. 6, pp. 773-781 | DOI
[7] Embedded crack vs. smeared crack models: a comparison of elementwise discontinuous crack path approaches with emphasis on mesh bias, Comput. Methods Appl. Mech. Eng., Volume 193 (2004) no. 30–32, pp. 3351-3375 | DOI | Zbl
[8] Evaluation of directional mesh bias in concrete fracture simulations using continuum damage models, Eng. Fract. Mech., Volume 75 (2008) no. 8, pp. 1921-1943 | DOI
[9] Why continuum damage is nonlocal: justification by quasiperiodic microcrack array, Mech. Res. Commun., Volume 14 (1987) no. 5–6, pp. 407-419 | DOI | Zbl
[10] Nonlocal integral formulations of plasticity and damage: survey of progress, J. Eng. Mech., Volume 128 (2002) no. 11, pp. 1119-1149
[11] On the microstructural origin of certain inelastic models, J. Eng. Mater. Technol., Volume 106 (1984) no. 4, pp. 326-330 | DOI
[12] Localization limiters in transient problems, Int. J. Solids Struct., Volume 24 (1988) no. 6, pp. 581-597 | DOI | Zbl
[13] The physics of plastic deformation, Int. J. Plast., Volume 3 (1987) no. 3, pp. 211-247 | DOI | Zbl
[14] A variational principle for gradient plasticity, Int. J. Solids Struct., Volume 28 (1991), pp. 845-857 | DOI | MR | Zbl
[15] Mécanique de l’endommagement. Théorie du premier gradient et application au béton, Ph. D. Thesis, Ecole Nationale des Ponts et Chaussées (1995)
[16] Gradient-enhanced damage model for quasi-brittle materials, Int. J. Numer. Methods Eng., Volume 39 (1996), pp. 391-403 | DOI | Zbl
[17] Delay-damage modelling for fracture prediction of laminated composites under dynamic loading, Eng. Trans., Volume 45 (1997) no. 1, pp. 29-46
[18] A delay damage mesomodel of laminates under dynamic loading: basic aspects and identification issues, Comput. Struct., Volume 81 (2003) no. 12, pp. 1177-1191 | DOI
[19] Delay-active damage versus non-local enhancement for anisotropic damage dynamics computations with alternated loading, Eng. Fract. Mech., Volume 77 (2010) no. 12, pp. 2294-2315 | DOI
[20] 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 | DOI | MR | Zbl
[21] Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, Volume 46 (1998) no. 8, pp. 1319-1342 | DOI | MR | Zbl
[22] Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, Volume 48 (2000) no. 4, pp. 797-826 | DOI | MR | Zbl
[23] Lipschitz regularization for softening material models: the Lip-field approach, C. R. Mécanique, Volume 349 (2021) no. 2, pp. 415-434 | DOI
[24] An experimental method for dynamic tensile testing of concrete by spalling, Int. J. Impact Eng., Volume 25 (2001), pp. 387-409 | DOI
[25] Spall experiments for the measurement of the tensile strength and fracture energy of concrete at high strain rates, Int. J. Impact Eng., Volume 32 (2006) no. 10, pp. 1635-1650 | DOI
[26] An experimental method to determine the tensile strength of concrete at high rates of strain, Exp. Mech., Volume 50 (2010) no. 7, pp. 941-955 | DOI
[27] Boundary effect on weight function in nonlocal damage model, Eng. Fract. Mech., Volume 76 (2009) no. 14, pp. 2217-2231 | DOI
[28] Incorrect initiation and propagation of failure in non-local and gradient-enhanced media, Int. J. Solids Struct., Volume 41 (2004) no. 2, pp. 351-363 | DOI | Zbl
[29] Why continuum damage is nonlocal: micromechanics arguments, J. Eng. Mech., Volume 117 (1991) no. 5, pp. 1070-1087
[30] Strain-based transient-gradient damage model for failure analyses, Comput. Methods Appl. Mech. Eng., Volume 160 (1998) no. 1–2, pp. 133-153 | DOI | Zbl
[31] Stress-based nonlocal damage model, Int. J. Solids Struct., Volume 48 (2011) no. 25–26, pp. 3431-3443 | DOI
[32] Nonlocal damage theory based on micromechanics of crack interactions, J. Eng. Mech., Volume 120 (1994), pp. 593-617
[33] Non-local damage model with evolving internal length, Int. J. Numer. Anal. Methods Geomech., Volume 28 (2004) no. 78, pp. 633-652 | DOI | Zbl
[34] Introduction of an internal time in nonlocal integral theories, 2007 (Internal Report LMT-Cachan. ENS Cachan/CNRS/Université Paris 6/PRES Unive 268)
[35] Non local damage model: boundary and evolving boundary effects, Eur. J. Environ. Civ. Eng., Volume 14 (2010) no. 6–7, pp. 729-749 | DOI
[36] A damage model with evolving nonlocal interactions, Int. J. Solids Struct., Volume 48 (2011) no. 10, pp. 1544-1559 | DOI | Zbl
[37] Nonlocal models with damage-dependent interactions motivated by internal time, Eng. Fract. Mech., Volume 142 (2015), pp. 255-275 | DOI
[38] From diffuse damage to strain localization from an Eikonal Non-Local (ENL) Continuum Damage model with evolving internal length, Comput. Methods Appl. Mech. Eng., Volume 331 (2018), pp. 650-674 | DOI | MR | Zbl
[39] Modeling and simulation of quasi-brittle failure with continuous anisotropic stress-based gradient-enhanced damage models, Comput. Methods Appl. Mech. Eng., Volume 332 (2018), pp. 644-685 | DOI | MR | Zbl
[40] Localization analysis of nonlocal models with damage-dependent nonlocal interaction, Int. J. Solids Struct., Volume 174–175 (2019), pp. 1-17 | DOI
[41] Time of rupture process under creep conditions (in Russian), Izv. Acad. Nauk, USSR, Volume 8 (1958), pp. 26-31
[42] Computational aspects of biaxial stress in plain reinforced concrete, Ph. D. Thesis, TU Delft (1993)
[43] Nonlocal models for damage and fracture: comparison of approaches, Int. J. Solids Struct., Volume 35 (1998) no. 31–32, pp. 4133-4145 | DOI | MR | Zbl
[44] A critical comparison of nonlocal and gradient-enhanced softening continua, Int. J. Solids Struct., Volume 38 (2001) no. 44–45, pp. 7723-7746 | DOI | Zbl
[45] A thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking, Comput. Methods Appl. Mech. Eng., Volume 193 (2004) no. 30–32, pp. 3403-3417 | DOI | Zbl
[46] Explicit and implicit gradient-enhanced damage models, Rev. Eur. Génie Civ., Volume 11 (2007) no. 7–8, pp. 1023-1044
[47] One-dimensional Eikonal Non-Local (ENL) damage models: influence of the integration rule for computing interaction distances and indirect loading control on damage localization, Mech. Res. Commun., Volume 110 (2020), 103620 | DOI
[48] A review of non local continuum damage: modelling of failure?, Netw. Heterog. Media, Volume 9 (2014) no. 4, pp. 575-597 | DOI | MR | Zbl
[49] Interaction-based non-local damage model for failure in quasi-brittle materials, Mech. Res. Commun., Volume 54 (2013), pp. 56-62 | DOI
[50] Path-following methods for unstable structural responses induced by strain softening: a critical review, C. R. Mécanique, Volume 350 (2022), pp. 205-236 | DOI
[51] Interpolation requirements for implicit gradient-enhanced continuum damage models, Commun. Numer. Methods Eng., Volume 19 (2003) no. 7, pp. 563-572 | DOI | Zbl
[52] A simple and unified implementation of phase field and gradient damage models, Adv. Model. Simul. Eng. Sci., Volume 5 (2018) no. 1, 15 | DOI
[53] A gradient-enhanced damage approach to fracture, J. Phys. IV France, Volume 6 (1996) no. C6, p. C6-491–C6-502 | DOI
[54] Wave propagation in a strain-softening bar: exact solution, J. Eng. Mech., Volume 111 (1985) no. 3, pp. 381-389
[55] Tensile strengths of silicon carbide (SiC) under shock loading (2001) no. ARL-TR-2430 (Technical report)
[56] Shock response of boron carbide (2001) no. ARL-TR-2456 (Technical report) | DOI
[57] Identification of strength and toughness of quasi-brittle materials from spall tests: a Sigma-point Kalman filter approach, Inverse Probl. Sci. Eng., Volume 27 (2019) no. 9, pp. 1318-1346 | DOI | MR | Zbl
[58] Computational modelling of impact damage in brittle materials, Int. J. Solids Struct., Volume 33 (1996) no. 20–22, pp. 2899-2938 | DOI | Zbl
[59] Micromorphic approach for gradient elasticity, viscoplasticity, and damage, J. Eng. Mech., Volume 135 (2009) no. 3, pp. 117-131
[60] From damage to fracture mechanics and conversely: a combined approach, Int. J. Solids Struct., Volume 33 (1996) no. 20–22, pp. 3327-3342 | DOI | Zbl
[61] Embedded crack model. Part II: combination with smeared cracks, Int. J. Numer. Methods Eng., Volume 50 (2001) no. 6, pp. 1291-1305 | DOI | Zbl
[62] From continuous to discontinuous failure in a gradient-enhanced continuum damage model, Comput. Methods Appl. Mech. Eng., Volume 192 (2003) no. 41–42, pp. 4581-4607 | DOI | Zbl
[63] A thermodynamic method for the construction of a cohesive law from a nonlocal damage model, Int. J. Solids Struct., Volume 46 (2009) no. 6, pp. 1476-1490 | DOI | Zbl
[64] A finite element approach coupling a continuous gradient damage model and a cohesive zone model within the framework of quasi-brittle failure, Comput. Methods Appl. Mech. Eng., Volume 237–240 (2012), pp. 244-259 | DOI | MR | Zbl
Cited by Sources:
Comments - Policy