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Stress resultant plasticity for shells revisited. (English) Zbl 1352.74172
Summary: In this work, we revisit the stress resultant elastoplastic geometrically exact shell finite element formulation that is based on the Ilyushin-Shapiro two-surface yield function with isotropic and kinematic hardening. The main focus is on implicit projection algorithms for computation of updated values of internal variables for stress resultant shell elastoplasticity. Four different algorithms are derived and compared. Three of them yield practically identical final results, yet they differ considerably in computational efficiency and implementation complexity, since they solve different sets of equations and they use different procedures that choose active yield surfaces. One algorithm does not provide acceptable accuracy. It turns out that the most simple and straightforward algorithm performs surprisingly well and efficiently. Several numerical examples are presented to illustrate the Ilyushin-Shapiro stress resultant shell formulation and the numerical performance of the presented integration algorithms.

74K25 Shells
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74B05 Classical linear elasticity
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[1] Hibbit, Karlsson, Sorensen, Abaqus Manuals, Abaqus 6.7, 2007.
[2] Başar, Y.; Itskov, M., Constitutive model and finite element formulation for large strain elasto-plastic analysis of shells, Comput. mech., 23, 466-481, (1999) · Zbl 0943.74035
[3] Bathe, K.J.; Dvorkin, E., A four-node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation, Int. J. numer. methods engrg., 21, 367-383, (1985) · Zbl 0551.73072
[4] Brank, B.; Perić, D.; Damjanić, F.B., On large deformation of thin elasto-plastic shells: implementation of a finite rotation model for quadrilateral shell elements, Int. J. numer. methods engrg., 40, 689-726, (1997) · Zbl 0892.73055
[5] Brank, B.; Ibrahimbegovic, A., On the relation between different parametrizations of finite rotations for shells, Engrg. comput., 18, 950-973, (2001) · Zbl 1017.74069
[6] Dujc, J.; Brank, B., On stress resultant plasticity and viscoplasticity for metal plates, Finite elem. anal. des., 44, 174-185, (2008)
[7] Ibrahimbegovic, A.; Brank, B.; Courtois, P., Stress resultant geometrically exact form of classical shell model and vector-like parametrization of constrained finite rotations, Int. J. numer. methods engrg., 52, 1235-1252, (2001) · Zbl 1112.74420
[8] Korelc, J., Automation of primal and sensitivity analysis of transient coupled problems, Comput. mech., 44, 631-649, (2009) · Zbl 1171.74043
[9] J. Korelc, AceGen, AceFem, 2012. Available from: <http://www.fgg.uni-lj.si/Symech>
[10] Simo, J.C.; Kennedy, J.G., On a stress resultant geometrically exact shell model. part V. nonlinear plasticity: formulation and integration algorithms, Comput. methods appl. mech. engrg., 96, 133-171, (1992) · Zbl 0754.73042
[11] Simo, J.C.; Hughes, T.J.R., Computational inelasticity, (1998), Springer · Zbl 0934.74003
[12] Crisfield, M.A.; Peng, X., Efficient nonlinear shell formulations with large rotations and plasticity, (), 1979-1997
[13] Shi, G.; Voyiadjis, G.Z., A simple non-layered finite element for the elasto-plastic analysis of shear flexible plates, Int. J. numer. methods engrg., 33, 85-100, (1992) · Zbl 0825.73824
[14] Ibrahimbegovic, A., Nonlinear solid mechanics: theoretical formulations and finite element solution methods, (2009), Springer · Zbl 1168.74002
[15] Voyiadjis, G.Z.; Woelke, P., General non-linear finite element analysis of thick plates and shells, Int. J. solidsand struct., 43, 2209-2242, (2006) · Zbl 1121.74478
[16] Skallerud, B.; Myklebust, L.I.; Haugen, B., Nonlinear response of shell structures: effects of plasticity modelling and large rotations, Thin-walled structures, 39, 463-482, (2001)
[17] Woelke, P.; Voyiadjis, G.Z.; Perzyna, P., Elasto-plastic finite element analysis of shells with damage due to microvoids, Int. J. numer. methods engrg., 68, 338-380, (2006) · Zbl 1158.74050
[18] Skallerud, B.; Haugen, B., Collapse of thin shell structures - stress resultant plasticity modelling with a co-rotated ADNES finite element formulation, Int. J. numer. methods engrg., 46, 1961-1986, (1999) · Zbl 0973.74081
[19] Dal Cortivo, N.; Felippa, C.A.; Bavestrello, H.; Silva, W.T.M., Plastic buckling and collapse of thin shell structures, using layered plastic modeling and co-rotational ANDES finite elements, Comput. methods appl. mech. engrg., 198, 785-798, (2009) · Zbl 1229.74042
[20] Zeng, Q.; Combescure, A.; Arnaudeau, F., An efficient plasticity algorithm for shell elements application to metal forming simulation, Comput. struct., 79, 1525-1540, (2001)
[21] Wagner, W.; Gruttmann, F., A robust non-linear mixed hybrid quadrilateral shell element, Int. J. numer. methods engrg., 64, 635-666, (2005) · Zbl 1122.74526
[22] Kim, K.D.; Lomboy, G.R., A co-rotational quasi-conforming 4-node resultant shell element for large deformation elasto-plastic analysis, Comput. methods appl. mech. engrg., 195, 6502-6522, (2006) · Zbl 1136.74042
[23] Simo, J.C.; Fox, D.D.; Rifai, M.S., On a stress resultant geometrically exact shell model. part III: computational aspects of the nonlinear theory, Comput. methods appl. mech. engrg., 79, 21-70, (1990) · Zbl 0746.73015
[24] Gould, P.L., Analysis of shells and plates, (1987), Springer · Zbl 0611.73074
[25] Areias, P.M.A.; Song, J.-H.; Belytschko, T., A finite strain quadrilateral shell element based on discrete Kirchhoff-love constraints, Int. J. numer. methods engrg., 64, 1166-1206, (2005) · Zbl 1113.74063
[26] Brank, B., Assessment of 4-node EAS-ANS shell elements for large deformation analysis, Comput. mech., 42, 39-51, (2008) · Zbl 1161.74049
[27] Bohinc, U.; Ibrahimbegovic, A.; Brank, B., Model adaptivity for finite element analysis of thin or thick plates based on equilibrated boundary stress resultants, Engrg. comput., 26, 66-99, (2009) · Zbl 1257.74147
[28] Kassiotis, C.; Ibrahimbegovic, A.; Matthies, H.G.; Brank, B., Stable splitting svheme for general form of associated plasticity including different scales of space and time, Comput. methods appl. mech. engrg., 199, 1254-1264, (2010) · Zbl 1227.74127
[29] Ghassemi, A.; Shahidi, A.; Farzin, M., A new element for analyzing large deformation of thin naghdi shell model. part II: plastic, Appl. math. model., 35, 2650-2668, (2011) · Zbl 1219.74003
[30] César de Sá, J.M.A.; Natal Jorge, R.M.; Fontes Valente, R.A.; Almeida Areias, P.M., Development of shear locking-free shell elements using an enhanced assumed strain formulation, Int. J. numer. methods engrg., 53, 1721-1750, (2002) · Zbl 1114.74484
[31] Wagner, W.; Klinkel, S.; Gruttmann, F., Elastic and plastic analysis of thin-walled structures using improved hexahedral elements, Comput. struct., 80, 857-869, (2002)
[32] Auricchio, F.; Taylor, R.L., A generalized elastoplastic plate theory and its algorithmic implementation, Int. J. numer. methods engrg., 37, 2583-2608, (1994) · Zbl 0808.73038
[33] Ibrahimbegovic, A.; Frey, F., Stress resultant finite element analysis of reinforced concrete plates, Engrg. comput., 10, 15-30, (1993)
[34] Ibrahimbegovic, A.; Colliat, J.B.; Davenne, L., Thermomechanical coupling in folded plates and non-smooth shells, Comput. methods appl. mech. engrg., 194, 2686-2707, (2005) · Zbl 1082.74014
[35] Colliat, J.B.; Ibrahimbegovic, A.; Davenne, L., Saint-Venant multi-surface plasticity model in strain space and stress resultants, Engrg. comput., 22, 536-557, (2005) · Zbl 1186.74099
[36] Bletzinger, K.-U.; Bischoff, M.; Ramm, E., A unified approach for shear-locking-free triangular and rectangular shell finite elements, Comput. struct., 75, 321-334, (2000)
[37] Brank, B., Nonlinear shell models with seven kinematic parameters, Comput. methods appl. mech. engrg., 194, 2336-2363, (2005) · Zbl 1082.74050
[38] Cirak, F.; Ortiz, M., Fully C^1-conforming subdivision elements for finite deformation thin-shell analysis, Int. J. numer. methods engrg., 51, 813-833, (2001) · Zbl 1039.74045
[39] Pimenta, P.M.; Campello, E.M.B., Shell curvature as an initial deformation: A geometrically exact finite element approach, Int. J. numer. methods engrg., 78, 1094-1112, (2009) · Zbl 1183.74306
[40] Brank, B.; Perić, D.; Damjanić, F.B., On implementation of a nonlinear four node shell finite element for multilayered elastic shells, Comput. mech., 16, 341-359, (1995) · Zbl 0848.73060
[41] Bischoff, M.; Ramm, E., Shear deformable shell elements for large strains and rotations, Int. J. numer. methods engrg., 40, 4427-4449, (1997) · Zbl 0892.73054
[42] Wriggers, P.; Eberlein, R.; Gruttmann, F., An axisymmetrical quasi-Kirchhoff-type shell element for large plastic deformations, Arch. appl. mech., 65, 1-14, (1995) · Zbl 0836.73077
[43] Betsch, P.; Sänger, N., On the use of geometrically exact shells in a conserving framework for flexible multibody dynamics, Comput. methods appl. mech. engrg., 198, 1609-1630, (2009) · Zbl 1227.74064
[44] Büchter, N.; Ramm, E., Shell theory versus degeneration - a comparison in large rotation shell analysis, Int. J. numer. methods engrg., 34, 39-59, (1992) · Zbl 0760.73041
[45] Ramm, E.; Wall, W.A., Shell structures - a sensitive interrelation between physics and numerics, Int. J. numer. methods engrg., 60, 381-427, (2004) · Zbl 1060.74572
[46] Sze, K.Y.; Liu, X.H.; Lo, S.H., Popular benchmark problems for geometrically nonlinear analysis of shells, Finite elem. anal. des., 40, 1551-1569, (2004)
[47] Matthies, H.G., A decomposition method for integration of the elastic-plastic rate problem, Int. J. numer. methods engrg., 28, 1-11, (1989) · Zbl 0669.73022
[48] Fuschi, P.; Perić, D.; Owen, D.R.J., Studies on generalized midpoint integration in rate-independent plasticity with reference to plane-stress J_2-flow theory, Comput. struct., 43, 1117-1133, (1992) · Zbl 0771.73023
[49] J. Dujc, Finite Element Analysis of Limit Load and Localized Failure of Structures, Doctoral Thesis, University of Ljubljana and ENS Cachan, 2010.
[50] Crisfield, M.A.; Peng, X., Instabilities induced by coarse meshes for nonlinear shell problem, Engrg. comput., 13, 110-114, (1996) · Zbl 0983.74575
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