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Isogeometric analysis of continuum damage in rotation-free composite shells. (English) Zbl 1423.74569
Summary: A large-deformation, isogeometric rotation-free Kirchhoff-Love shell formulation is equipped with a damage model to efficiently and accurately simulate progressive failure in laminated composite structures. The damage model consists of Hashin’s theory of damage initiation, a bilinear material model for damage evolution, and an appropriately chosen Gibbs free-energy density. Four intralaminar modes of failure are considered: Longitudinal and transverse tension, and longitudinal and transverse compression. The choice of shell formulation and modes of failure modeled make the proposed methodology valid in the regime of relatively thin shell structures where damage occurs without significant evidence of delamination. The damage model is extensively validated against experimental data and its use is also illustrated in the context of multiscale composite damage analysis.

MSC:
74K25 Shells
65D17 Computer-aided design (modeling of curves and surfaces)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74R05 Brittle damage
Software:
ABAQUS; DDDAS
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[1] Fish, J.; Yu, Q., Two-scale damage modeling of brittle composites, Compos. Sci. Technol., 61, 2215-2222, (2001)
[2] Kruch, S.; Chaboche, J. L.; Pottier, T., Two-scale viscoplastic and damage analysis of metal matrix composite, Stud. Appl. Mech., 44, 45-56, (1996)
[3] Fish, J.; Yu, Q., Computational damage mechanics for composite materials based on mathematical homogenization, Internat. J. Numer. Methods Engrg., 45, 1657-1679, (1999) · Zbl 0949.74057
[4] Alfaroa, M. V.C.; Suiker, A. S.J.; Verhoosel, C. V.; de Borst, R., Numerical homogenization of cracking processes in thin fibre-epoxy layers, Eur. J. Mech. A Solids, 29, 119-131, (2010)
[5] Raghavan, P.; Li, S.; Ghosh, S., Two scale response and damage modeling of composite materials, Finite Elem. Anal. Des., 40, 1619-1640, (2004)
[6] Swaminathan, S.; Ghosh, S.; Pagano, N. J., Statistically equivalent representative volume elements for composite microstructures, part i: without damage, J. Compos. Mater., 40, 583-604, (2006)
[7] Swaminathan, S.; Ghosh, S., Statistically equivalent representative volume elements for composite microstructures, part ii: with evolving damage, J. Compos. Mater., 40, 605-621, (2006)
[8] Pijaudier-Cabot, G.; Bazant, Z. P., Nonlocal damage theory, J. Eng. Mech., 113, 1512-1533, (1987)
[9] Bazant, Z. P.; Pijaudier-Cabot, G., Nonlocal continuum damage, localization instability and convergence, J. Appl. Mech., 55, 287-293, (1988) · Zbl 0663.73075
[10] de Borst, R.; Pamin, J.; Peerlings, R. H.J.; Sluys, L. J., Strain-based transient-gradient damage model for failure analyses, Comput. Mech., 17, 130-141, (1995) · Zbl 0840.73047
[11] Geers, M. G.D.; de Borst, R.; Brekelmans, W. A.M.; Peerlings, R. H.J., Strain-based transient-gradient damage model for failure analyses, Comput. Methods Appl. Mech. Engrg., 160, 133-153, (1998) · Zbl 0938.74006
[12] Verhoosel, C. V.; Scott, M. A.; Hughes, T. J.R.; de Borst, R., An isogeometric analysis approach to gradient damage models, Internat. J. Numer. Methods Engrg., 86, 115-134, (2011) · Zbl 1235.74320
[13] Hughes, T. J.R.; Cottrell, J. A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 4135-4195, (2005) · Zbl 1151.74419
[14] Cottrell, J. A.; Hughes, T. J.R.; Bazilevs, Y., Isogeometric analysis: toward integration of CAD and FEA, (2009), Wiley Chichester · Zbl 1378.65009
[15] Piegl, L.; Tiller, W., The NURBS book (monographs in visual communication), (1997), Springer-Verlag New York
[16] Hosseini, S.; Remmers, J. J.C.; de Borst, R., The incorporation of gradient damage models in shell elements, Comput. Methods Appl. Mech. Engrg., 98, 391-398, (2014) · Zbl 1352.74273
[17] Bazilevs, Y.; Marsden, A. L.; Lanza di Scalea, F.; Majumdar, A.; Tatineni, M., Toward a computational steering framework for large-scale composite structures based on continually and dynamically injected sensor data, Procedia Comput. Sci., 9, 1149-1158, (2012)
[18] Kiendl, J.; Bletzinger, K.-U.; Linhard, J.; Wüchner, R., Isogeometric shell analysis with Kirchhoff-love elements, Comput. Methods Appl. Mech. Engrg., 198, 3902-3914, (2009) · Zbl 1231.74422
[19] Kiendl, J.; Bazilevs, Y.; Hsu, M.-C.; Wüchner, R.; Bletzinger, K.-U., The bending strip method for isogeometric analysis of Kirchhoff-love shell structures comprised of multiple patches, Comput. Methods Appl. Mech. Engrg., 199, 2403-2416, (2010) · Zbl 1231.74482
[20] Benson, D. J.; Bazilevs, Y.; Hsu, M.-C.; Hughes, T. J.R., Isogeometric shell analysis: the Reissner-Mindlin shell, Comput. Methods Appl. Mech. Engrg., 199, 276-289, (2010) · Zbl 1227.74107
[21] Benson, D. J.; Bazilevs, Y.; Hsu, M.-C.; Hughes, T. J.R., A large deformation, rotation-free, isogeometric shell, Comput. Methods Appl. Mech. Engrg., 200, 1367-1378, (2011) · Zbl 1228.74077
[22] Benson, D. J.; Hartmann, S.; Bazilevs, Y.; Hsu, M.-C.; Hughes, T. J.R., Blended isogeometric shells, Comput. Methods Appl. Mech. Engrg., 255, 133-146, (2013) · Zbl 1297.74114
[23] Echter, R.; Oesterle, B.; Bischoff, M., A hierarchic family of isogeometric shell finite elements, Comput. Methods Appl. Mech. Engrg., 254, 170-180, (2013) · Zbl 1297.74071
[24] Bazilevs, Y.; Hsu, M.-C.; Kiendl, J.; Wüchner, R.; Bletzinger, K.-U., 3D simulation of wind turbine rotors at full scale. part II: fluid-structure interaction modeling with composite blades, Internat. J. Numer. Methods Fluids, 65, 236-253, (2011) · Zbl 1428.76087
[25] Bazilevs, Y.; Hsu, M.-C.; Kiendl, J.; Benson, D. J., A computational procedure for prebending of wind turbine blades, Internat. J. Numer. Methods Engrg., 89, 323-336, (2012) · Zbl 1242.74026
[26] Lapczyk, I.; Hurtado, J. A., Progressive damage modeling in fiber-reinforced materials, Composites A, 38, 2333-2341, (2007)
[27] Hashin, Z.; Rotem, A., A fatigue criterion for fiber-reinforced materials, J. Compos. Mater., 7, 448-464, (1973)
[28] Matzenmiller, A.; Lubliner, J.; Taylor, R. L., A constitutive model for anisotropic damage in fiber-composites, Mech. Mater., 20, 125-152, (1995)
[29] Soares, C. A.M.; Soares, C. M.M.; Freitas, M. J.M., Mechanics of composite materials and structures, (1998), Kluwer Academic Publishers
[30] Bischoff, M.; Wall, W. A.; Bletzinger, K.-U; Ramm, E., Models and finite elements for thin-walled structures, (Stein, E.; de Borst, R.; Hughes, T. J.R., Encyclopedia of Computational Mechanics, Solids, Structures and Coupled Problems, vol. 2, (2004), Wiley), (Chapter 3)
[31] Bletzinger, K. U.; Firl, M.; Linhard, J.; Wüchner, R., Optimal shapes of mechanically motivated surfaces, Comput. Methods Appl. Mech. Engrg., 199, 324-333, (2010) · Zbl 1227.74043
[32] Bletzinger, K. U.; Wüchner, R.; Daoud, F.; Camprubí, N., Computational methods for form finding and optimization of shells and membranes, Comput. Methods Appl. Mech. Engrg., 194, 3438-3452, (2005) · Zbl 1092.74032
[33] Oñate, E.; Zarate, F., Rotation-free triangular plate and shell elements, Internat. J. Numer. Methods Engrg., 47, 557-603, (2000) · Zbl 0968.74070
[34] Cirak, F.; Ortiz, M., Fully \(C^1\)-conforming subdivision elements for finite deformation thin-shell analysis, Internat. J. Numer. Methods Engrg., 51, 813-833, (2001) · Zbl 1039.74045
[35] Linhard, J.; Wüchner, R.; Bletzinger, K. U., “upgrading” membranes to shells—the CEG rotation free shell element and its application in structural analysis, Finite Elem. Anal. Des., 44, 63-74, (2007)
[36] Belytschko, T.; Liu, W. K.; Moran, B., Nonlinear finite elements for continua and structures, (2000), Wiley · Zbl 0959.74001
[37] Reddy, J. N., Mechanics of laminated composite plates and shells: theory and analysis, (2004), CRC Press Boca Raton, FL · Zbl 1075.74001
[38] Davila, C. G.; Rose, C. A., Lecture note: progressive damage analysis of composites, (Aircraft Aging and Durability Project, (2007), NASA Brussels, Belgium)
[39] Daniel, I. M.; Ishai, O., Engineering mechanics of composite materials, (1994), Oxford University Press New York, NY
[40] Pinho, S. T., Modeling failure of laminated composites using physically-based failure models, (2005), Imperial College London, (Ph.D. thesis)
[41] Maimi, P.; Camanho, P. P.; Mayugo, J. A.; Davila, C. G., A continuum damage model for composite laminates: part i—constitutive model, Mech. Mater., 39, 897-908, (2007)
[42] Maimi, P.; Camanho, P. P.; Mayugo, J. A.; Davila, C. G., A continuum damage model for composite laminates: part ii—computational implementation and validation, Mech. Mater., 39, 909-919, (2007)
[43] Murakami, A., Mechanical modeling of material damage, J. Appl. Mech. Trans. ASME, 55, 280-286, (1988)
[44] Song, S. H.; Paulino, G. H.; Buttlar, W. G., Influence of the cohesive zone model shape parameter on asphalt concrete fracture behavior, AIP Conf. Proc., 973, 730-735, (2008)
[45] Hinton, M. J.; Soden, P. D., Predicting of failure in composite laminate: the background to the exercise, Compos. Sci. Technol., 58, 1001, (1998)
[46] Soden, P. D.; Hinton, M. J.; Kaddour, A. S., Lamina properties, lay-up configurations and loading conditions for a range of fiber-reinforced composite laminates, Compos. Sci. Technol., 58, 1011-1022, (1998)
[47] Soden, P. D.; Hinton, M. J.; Kaddour, A. S., A comparison of the predictive capabilities of current failure theories for composite laminates, Compos. Sci. Technol., 58, 1225-1254, (1998)
[48] Soden, P. D.; Hinton, M. J.; Kaddour, A. S., Biaxial test result for strength and deformation of a range of e-Glass and carbon fiber reinforced composite laminates: failure exercise benchmark data, Compos. Sci. Technol., 62, 1489-1514, (2002)
[49] Green, B. G.; Wisnom, M. R.; Hallett, S. R., An experimental investigation into tensile strength scaling of notched composites, Composites, 38, 867-878, (2007)
[50] Hallett, S. R.; Green, B. G.; Jiang, W. G.; Wisnom, M. R., An experimental and numerical investigation into the damage mechanisms in notched composites, Composites A, 40, 619-624, (2009)
[51] Swindeman, M. J.; Iarve, E. V.; Brockman, R. A.; Mollenhauer, D. H.; Hallett, S. R., Strength prediction in open hole composite laminates by using discrete damage modeling, AIAA J., 51, 936-945, (2013)
[52] Chung, J.; Hulbert, G. M., A time integration algorithm for structural dynamics withimproved numerical dissipation: the generalized-\(\alpha\) method, J. Appl. Mech., 60, 371-375, (1993) · Zbl 0775.73337
[53] Sun, C. T.; Vaidya, R. S., Prediction of composite properties from a representative volume element, Compos. Sci. Technol., 56, 171-179, (1996)
[54] Daniel, I. M.; Ishai, O., Engineering mechanics of composite materials, (2006), Oxford University Press
[55] ABAQUS Inc. ABAQUS 6.10 User’s manual. Providence, RI, USA, 2010.
[56] Verhoosel, C. V.; Scott, M. A.; de Borst, R.; Hughes, T. J.R., An isogeometric approach to cohesive zone modeling, Internat. J. Numer. Methods Engrg., 87, 336-360, (2011) · Zbl 1242.74169
[57] De Luycker, E.; Benson, D. J.; Belytschko, T.; Bazilevs, Y.; Hsu, M.-C., X-FEM in isogeometric analysis for linear fracture mechanics, Internat. J. Numer. Methods Engrg., 87, 541-565, (2011) · Zbl 1242.74105
[58] Borden, M. J.; Scott, M. A.; Verhoosel, C. V.; Hughes, T. J.R.; Landis, C. M., A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Engrg., 217-220, 77-95, (2012) · Zbl 1253.74089
[59] Darema, F., Dynamic data driven applications systems: A new paradigm for application simulations and measurements, (Proceedings of ICCS 2004 4th International Conference on Computational Science, (2004)), 662-669
[60] Hosseini, S.; Remmers, J. J.C.; Verhoosel, C. V.; de Borst, R., An isogeometric solid-like shell element for non-linear analysis, Internat. J. Numer. Methods Engrg., 95, 238-256, (2013) · Zbl 1352.74362
[61] Hosseini, S.; Remmers, J. J.C.; Verhoosel, C. V.; de Borst, R., An isogeometric continuum shell element for non-linear analysis, Comput. Methods Appl. Mech. Engrg., 271, 1-22, (2014) · Zbl 1296.74057
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