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A large strain gradient-enhanced ductile damage model: finite element formulation, experiment and parameter identification. (English) Zbl 1457.74018
Summary: A gradient-enhanced ductile damage model at finite strains is presented, and its parameters are identified so as to match the behaviour of DP800. Within the micromorphic framework, a multi-surface model coupling isotropic Lemaitre-type damage to von Mises plasticity with nonlinear isotropic hardening is developed. In analogy to the effective stress entering the yield criterion, an effective damage driving force – increasing with increasing plastic strains – entering the damage dissipation potential is proposed. After an outline of the basic model properties, the setup of the (micro)tensile experiment is discussed and the importance of including unloading for a parameter identification with a material model including damage is emphasised. Optimal parameters, based on an objective function including measured forces and the displacement field obtained from digital image correlation, are identified. The response of the proposed model is compared to a tensile experiment of a specimen with a different geometry as a first approach to validate the identified parameters.
74A45 Theories of fracture and damage
74M25 Micromechanics of solids
74S05 Finite element methods applied to problems in solid mechanics
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[1] Voyiadjis, GZ; Al-Rub, R. K Abu; Voyiadjis, G. Z., Gradient-enhanced coupled plasticity-anisotropic damage model for concrete fracture: computational aspects and applications, Int. J. Damage Mech., 18, 2, 115-154 (2009)
[2] Anderson, D.; Butcher, C.; Pathak, N.; Worswick, MJ, Failure parameter identification and validation for a dual-phase 780 steel sheet, Int. J. Solids Struct., 124, 89-107 (2017)
[3] Anduquia-Restrepo, J.; Narváez-Tovar, C.; Rodríguez-Baracaldo, R., Computational and numerical analysis of ductile damage evolution under a load-unload tensile test in dual-phase steel, Strojniski Vestnik/J. Mech. Eng., 64, 5, 339-348 (2018)
[4] Avril, S.; Bonnet, M.; Bretelle, A-S; Grédiac, M.; Hild, F.; Ienny, P.; Latourte, F.; Lemosse, D.; Pagano, S.; Pagnacco, E.; Pierron, F., Overview of identification methods of mechanical parameters based on full-field measurements, Exp. Mech., 48, 4, 381 (2008)
[5] Balieu, R.; Kringos, N., A new thermodynamical framework for finite strain multiplicative elastoplasticity coupled to anisotropic damage, Int. J. Plast., 70, 126-150 (2015)
[6] Bažant, ZP; Belytschko, TB; Chang, T-P, Continuum theory for strain-softening, J. Eng. Mech., 110, 12, 1666-1692 (1984)
[7] Bažant, ZP; Pijaudier-Cabot, G., Nonlocal continuum damage, localization instability and convergence, J. Appl. Mech., 55, 2, 287-293 (1988) · Zbl 0663.73075
[8] Besson, J., Continuum models of ductile fracture: a review, Int. J. Damage Mech, 19, 1, 3-52 (2010)
[9] Betten, J., Applications of tensor functions in continuum damage mechanics, Int. J. Damage Mech., 1, 1, 47-59 (1992)
[10] Brepols, T.; Wulfinghoff, S.; Reese, S., Gradient-extended two-surface damage-plasticity: micromorphic formulation and numerical aspects, Int. J. Plast., 97, Supplement C, 64-106 (2017)
[11] Brepols, T.; Wulfinghoff, S.; Reese, S., A gradient-extended two-surface damage-plasticity model for large deformations, Int. J. Plast., 129, 102635 (2020)
[12] Cao, T-S; Mazière, M.; Danas, K.; Besson, J., A model for ductile damage prediction at low stress triaxialities incorporating void shape change and void rotation, Int. J. Solids Struct., 63, 240-263 (2015)
[13] Chaboche, J-L, Development of continuum damage mechanics for elastic solids sustaining anisotropic and unilateral damage, Int. J. Damage Mech., 2, 4, 311-329 (1993)
[14] De Borst, R.; Sluys, LJ; Muhlhaus, H-B; Pamin, J., Fundamental issues in finite element analyses of localization of deformation, Eng. Comput., 10, 2, 99-121 (1993)
[15] de Souza Neto, E. A.; Owen, D. R J.; Perić, D., Computational Methods for Plasticity (2008), Chichester: Wiley, Chichester
[16] Dimitrijevic, BJ; Hackl, K., A method for gradient enhancement of continuum damage models, Technische Mechanik, 28, 1, 43-52 (2008)
[17] Ekh, M.; Menzel, A.; Runesson, K.; Steinmann, P., Anisotropic damage with the MCR effect coupled to plasticity, Int. J. Eng. Sci., 41, 13-14, 1535-1551 (2003) · Zbl 1211.74019
[18] Forest, S., Micromorphic approach for gradient elasticity, viscoplasticity, and damage, J. Eng. Mech., 135, 3, 117-131 (2009)
[19] Guhr, F.; Sprave, L.; Barthold, F-J; Menzel, A., Computational shape optimisation for a gradient-enhanced continuum damage model, Comput. Mech., 65, 4, 1105-1124 (2020) · Zbl 07185497
[20] Gurson, AL, Continuum theory of ductile rupture by void nucleation and growth: Part I-Yield criteria and flow rules for porous ductile media, J. Eng. Mater. Technol., 99, 1, 2-15 (1977)
[21] Junker, P.; Schwarz, S.; Jantos, DR; Hackl, K., A fast and robust numerical treatment of a gradient-enhanced model for brittle damage, Int. J. Multiscale Comput. Eng., 17, 2, 151-180 (2019)
[22] Kachanov, L., On time to rupture in creep conditions [in russian], izv, AN SSSR, OTN, 8, 26-31 (1958)
[23] Kattan, PI; Voyiadjis, GZ, A coupled theory of damage mechanics and finite strain elasto-plasticity—I. Damage and elastic deformations, Int. J. Eng. Sci., 28, 5, 421-435 (1990) · Zbl 0728.73038
[24] Kiefer, B.; Waffenschmidt, T.; Sprave, L.; Menzel, A., A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts, Int. J. Damage Mech., 27, 2, 253-295 (2018)
[25] Krajcinovic, D.; Krajcinovic, D., Continuum models, Damage Mechanics, Volume 41 of North-Holland Series in Applied Mathematics and Mechanics, chapter 4, 415-602 (1996), Amsterdam: North-Holland, Amsterdam
[26] Kusche, C.; Reclik, T.; Freund, M.; Al-Samman, Talal; Kerzel, U.; Korte-Kerzel, S., Large-area, high-resolution characterisation and classification of damage mechanisms in dual-phase steel using deep learning, PLoS One, 14, 5, e0216493 (2019)
[27] Kusche, CF; Dunlap, A.; Pütz, F.; Tian, Chunhua; Kirchlechner, C.; Aretz, A.; Schwedt, A.; Al-Samman, Talal; Münstermann, S.; Korte-Kerzel, S., Efficient characterization tools for deformation-induced damage at different scales, Prod. Eng. Res. Devel., 14, 1, 95-104 (2019)
[28] Lämmer, H.; Tsakmakis, Ch, Discussion of coupled elastoplasticity and damage constitutive equations for small and finite deformations, Int. J. Plast., 16, 5, 495-523 (2000) · Zbl 0976.74005
[29] Langenfeld, K.; Mosler, J., A micromorphic approach for gradient-enhanced anisotropic ductile damage, Comput. Methods Appl. Mech. Eng., 360, 112717 (2020) · Zbl 1441.74020
[30] Leckie, FA; Onat, ET; Hult, J.; Lemaitre, J., Tensorial nature of damage measuring internal variables, Phys. Non-Linear. Struct. Anal., 140-155 (1981), Berlin: Springer, Berlin
[31] Lemaitre, J., A Continuous Damage Mechanics Model for Ductile Fracture, J. Eng. Mater. Technol., 107, 1, 83-89 (1985)
[32] Lemaitre, J., A Course on Damage Mechanics (1996), Berlin: Springer, Berlin · Zbl 0852.73003
[33] Lemaitre, J.; Dufailly, J., Damage measurements, Eng. Fract. Mech., 28, 5, 643-661 (1987)
[34] Liebe, T.; Menzel, A.; Steinmann, P., Theory and numerics of geometrically non-linear gradient plasticity, Int. J. Eng. Sci., 41, 13-14, 1603-1629 (2003) · Zbl 1211.74042
[35] Liebe, T.; Steinmann, P.; Benallal, A., Theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage, Comput. Methods Appl. Mech. Eng., 190, 49-50, 6555-6576 (2001) · Zbl 0991.74010
[36] Ling, Chao; Forest, Samuel; Besson, Jacques; Tanguy, Benoît; Latourte, Felix, A reduced micromorphic single crystal plasticity model at finite deformations. application to strain localization and void growth in ductile metals, Int. J. Solids Struct., 134, 43-69 (2018)
[37] Mahnken, R.; Kuhl, E., Parameter identification of gradient enhanced damage models with the finite element method, Eur. J. Mech. A. Solids, 18, 5, 819-835 (1999) · Zbl 0966.74065
[38] Mahnken, R.; Stein, E., Parameter identification for finite deformation elasto-plasticity in principal directions, Comput. Methods Appl. Mech. Eng., 147, 1, 17-39 (1997) · Zbl 0896.73024
[39] Markiewicz, É.; Langrand, B.; Notta-Cuvier, D., A review of characterisation and parameters identification of materials constitutive and damage models: from normalised direct approach to most advanced inverse problem resolution, Int. J. Impact Eng., 110, 371-381 (2017)
[40] McVeigh, C.; Vernerey, F.; Liu, Wing Kam; Moran, B.; Olson, G., An interactive micro-void shear localization mechanism in high strength steels, J. Mech. Phys. Solids, 55, 2, 225-244 (2007)
[41] Menzel, A.; Steinmann, P., A theoretical and computational framework for anisotropic continuum damage mechanics at large strains, Int. J. Solids Struct., 38, 52, 9505-9523 (2001) · Zbl 1045.74006
[42] Menzel, A.; Steinmann, P., Geometrically non-linear anisotropic inelasticity based on fictitious configurations: application to the coupling of continuum damage and multiplicative elasto-plasticity, Int. J. Numer. Meth. Eng., 56, 14, 2233-2266 (2003) · Zbl 1038.74512
[43] Murakami, S., Mechanical modeling of material damage, J. Appl. Mech., 55, 2, 280-286 (1988)
[44] Murakami, S., Continuum Damage Mechanics: A Continuum Mechanics Approach to the Analysis of Damage and Fracture (Solid Mechanics and Its Applications) (2012), Berlin: Springer, Berlin
[45] Nguyen, Tuan H. A.; Bui, Tinh Quoc; Hirose, Sohichi, Smoothing gradient damage model with evolving anisotropic nonlocal interactions tailored to low-order finite elements, Comput. Methods Appl. Mech. Eng., 328, 498-541 (2018) · Zbl 1439.74337
[46] Nguyen, V-D; Lani, F.; Pardoen, T.; Morelle, XP; Noels, L., A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers, Int. J. Solids Struct., 96, 192-216 (2016)
[47] Ostwald, R.; Kuhl, E.; Menzel, A., On the implementation of finite deformation gradient-enhanced damage models, Comput. Mech., 64, Issue 3, 847-877 (2019) · Zbl 07099904
[48] Peerlings, RHJ; de Borst, R.; Brekelmans, WAM; de Vree, JHP; Spee, I., Some observations on localisation in non-local and gradient damage models, Eur. J. Mech. A/Solids, 15, 937-953 (1996) · Zbl 0891.73055
[49] Polindara, C.; Waffenschmidt, T.; Menzel, A., A computational framework for modelling damage-induced softening in fibre-reinforced materials—application to balloon angioplasty, Int. J. Solids Struct., 118-119, 235-256 (2017)
[50] Rabotnov, Y.N.: Creep problems in structural members, volume 7 of North-Holland Series in Applied Mathematics and Mechanics. North-Holland, Amsterdam, 1969. Trans. from the Russian · Zbl 0184.51801
[51] Rose, L.; Menzel, A., Optimisation based material parameter identification using full field displacement and temperature measurements, Mech. Mater., 145, 103292 (2020)
[52] Rousselier, G., Ductile fracture models and their potential in local approach of fracture, Nucl. Eng. Des., 105, 1, 97-111 (1987)
[53] Roux, E.; Bouchard, P-O, On the interest of using full field measurements in ductile damage model calibration, Int. J. Solids Struct., 72, 50-62 (2015)
[54] Sabnis, PA; Forest, S.; Cormier, J., Microdamage modelling of crack initiation and propagation in FCC single crystals under complex loading conditions, Comput. Methods Appl. Mech. Eng., 312, 468-491 (2016) · Zbl 1439.74241
[55] Seupel, A.; Hütter, G.; Kuna, M., An efficient FE-implementation of implicit gradient-enhanced damage models to simulate ductile failure, Eng. Fract. Mech., 199, 41-60 (2018)
[56] Simo, JC; Ciarlet, PG; Lions, JL, Numerical analysis and simulation of plasticity, Numerical Methods for Solids (Part 3) Numerical Methods for Fluids (Part 1), 183-499 (1998), Amsterdam: Elsevier, Amsterdam
[57] Steinmann, P., Formulation and computation of geometrically non-linear gradient damage, Int. J. Numer. Meth. Eng., 46, 5, 757-779 (1999) · Zbl 0978.74006
[58] Steinmann, P.; Stein, E., A unifying treatise of variational principles for two types of micropolar continua, Acta Mech., 121, 1-4, 215-232 (1997) · Zbl 0878.73004
[59] Triantafyllidis, N.; Aifantis, EC, A gradient approach to localization of deformation. I. hyperelastic materials, J. Elast., 16, 3, 225-237 (1986) · Zbl 0594.73044
[60] Tvergaard, V.; Needleman, A., Analysis of the cup-cone fracture in a round tensile bar, Acta Metall., 32, 1, 157-169 (1984)
[61] Vandoren, B.; Simone, A., Modeling and simulation of quasi-brittle failure with continuous anisotropic stress-based gradient-enhanced damage models, Comput. Methods Appl. Mech. Eng., 332, 644-685 (2018) · Zbl 1440.74348
[62] Waffenschmidt, T.; Polindara, C.; Menzel, A.; Blanco, S., A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials, Comput. Methods Appl. Mech. Eng., 268, 801-842 (2014) · Zbl 1295.74007
[63] Wcisło, B.; Pamin, J.; Kowalczyk-Gajewska, K., Gradient-enhanced damage model for large deformations of elastic-plastic materials, Arch. Mech., 65, 5, 407-428 (2013) · Zbl 1446.74208
[64] Wulfinghoff, S.; Fassin, M.; Reese, S., A damage growth criterion for anisotropic damage models motivated from micromechanics, Int. J. Solids Struct., 121, 21-32 (2017)
[65] Xu, Yanjie; Poh, Leong Hien, Localizing gradient-enhanced Rousselier model for ductile fracture, Int. J. Numer. Meth. Eng., 119, 9, 826-851 (2019)
[66] Zhang, Yi; Lorentz, E.; Besson, J., Ductile damage modelling with locking-free regularised gtn model, Int. J. Numer. Meth. Eng., 113, 13, 1871-1903 (2018)
[67] Zhu, Yazhi; Engelhardt, MD, A nonlocal triaxiality and shear dependent continuum damage model for finite strain elastoplasticity, Eur. J. Mech. A. Solids, 71, 16-33 (2018) · Zbl 1406.74125
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