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An objective incremental formulation for the solution of anisotropic elastoplastic problems at finite strain. (English) Zbl 1017.74070

Summary: This paper presents an objective formulation for anisotropic elastic-plastic problems at large strain plasticity. The constitutive equations are written in a rotating frame, the multiplicative decomposition of deformation gradient is adopted, and the formulation is hyperelastic. Since no stress rates are present and the incremental constitutive law is formulated in a rotating frame, the formulation is numerically objective in time integration. Explicit algorithm is proposed and is optimized with regard to stability and accuracy. The incremental law is integrated in fast Lagrangian analysis of continua (FLAC) method to model anisotropic elastic-plastic problems at finite strain. Structural tests are carried out for isotropic and orthotropic materials.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
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[1] Mandel, Plasticité classique et viscoplasticité, Course and Lectures 97 (1971)
[2] Dafalias, The Plastic spin, Journal of Applied Mechanics ASME 52 pp 865– (1985) · Zbl 0587.73052 · doi:10.1115/1.3169160
[3] Dafalias, Plastic spin: necessity or redundancy, International Journal of Plasticity 9 pp 909– (1998) · Zbl 0947.74008 · doi:10.1016/S0749-6419(98)00036-9
[4] Dogui A Plasticité anisotrope en grandes déformations 1989
[5] Dogui, Quelques remarques sur la plasticité anisotrope en grandes déformations, Comptes Rendusde l’ Academie des Sciences Paris 299 (18) pp 1225– (1984)
[6] Lo, Stress evaluation algorithms for rate constitutive equations in finite deformation analysis, International Journal for Numerical Methods in Engineering 26 pp 121– (1988) · Zbl 0654.73052 · doi:10.1002/nme.1620260109
[7] Lush, An implicit time-integration procedure for a set of internal variable constitutive equations for isotropic elasto-viscoplasticity, International Journal of Plasticity 5 pp 521– (1989) · Zbl 0695.73009 · doi:10.1016/0749-6419(89)90012-0
[8] Moss, On instabilities in large deformation simple shear loading, Computer Methods in Applied Mechanics and Engineering 46 pp 329– (1984) · Zbl 0549.73027 · doi:10.1016/0045-7825(84)90108-7
[9] Nagtegaal, On the implementation of inelastic constitutive equations with special reference to large deformation problems, Computer Methods in Applied Mechanics and Engineering 33 pp 469– (1982) · Zbl 0492.73077 · doi:10.1016/0045-7825(82)90120-7
[10] Arif, On the performance of two tangent operators for finite element analysis of large deformation inelastic problems, International Journal for Numerical Methods in Engineering 35 pp 369– (1992) · Zbl 0768.73067 · doi:10.1002/nme.1620350209
[11] Tuğcu, On the implementation of anisotropic yield functions into finite strain problems of sheet metal forming, International Journal of Plasticity 15 pp 1021– (1999) · Zbl 0944.74016 · doi:10.1016/S0749-6419(99)00023-6
[12] Yoon, A general elasto-plastic finite element formulation based on incremental deformation theory for planar anisotropy and its application to sheet metal forming, International Journal of Plasticity 15 pp 35– (1999) · Zbl 1054.74063 · doi:10.1016/S0749-6419(98)00059-X
[13] Mauget, A large displacement formulation for anisotropic constitutive laws, European Journal of Mechanics A/Solids 18 pp 859– (1999) · Zbl 0971.74018 · doi:10.1016/S0997-7538(99)00130-8
[14] Lee, Elastic-plastic deformation at finite strain, Journal of Applied Mechanics ASME 36 pp 1– (1969) · Zbl 0179.55603 · doi:10.1115/1.3564580
[15] Xia, Hypoelasticity model based upon the logarithmic stress rate, Journal of Elasticity 47 pp 51– (1997) · Zbl 0888.73011 · doi:10.1023/A:1007356925912
[16] Xia, On objective corotational rates and their defining spin tensors, International Journal of Solids and Structures 35 pp 4001– (1998) · Zbl 0936.74012 · doi:10.1016/S0020-7683(97)00267-9
[17] Kojic, Studies of finite element procedures-stress solution of a closed elastic strain path with stretching and shearing using the updated Lagrangian formulation, Computers and Structures 26 pp 175– (1987) · Zbl 0609.73074 · doi:10.1016/0045-7949(87)90247-1
[18] Bruhns, Self consistent Eulerian rate type elasto-plasticity models based upon the logarithmic stress rate, International Journal of Plasticity 15 pp 479– (1999) · Zbl 1036.74010 · doi:10.1016/S0749-6419(99)00003-0
[19] Eterovic, A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures, International Journal for Numerical Methods in Engineering 30 pp 1099– (1990) · Zbl 0714.73035 · doi:10.1002/nme.1620300602
[20] Hill, Advances in Applied Mechanics 19 pp 1– (1978)
[21] Xia, Logarithmic strain, logarithmic spin and logarithmic rate, Acta Mechanica 124 pp 89– (1997) · Zbl 0909.73006 · doi:10.1007/BF01213020
[22] Auricchio, A return-map algorithm for general associative isotropic elasto-plastic materials in large deformation regimes, International Journal of Plasticity 15 pp 1359– (1999) · Zbl 0957.74078 · doi:10.1016/S0749-6419(99)00044-3
[23] Hughes, Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis, International Journal for Numerical Methods in Engineering 15 pp 1862– (1980) · Zbl 0463.73081 · doi:10.1002/nme.1620151210
[24] Rubinstein, Objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses, Computer Methods in Applied Mechanics and Engineering 36 pp 277– (1983) · Zbl 0486.73081 · doi:10.1016/0045-7825(83)90125-1
[25] Chatti S Dogui A Sidoroff F Lois incrémentales explicites en grandes déformations élastoplastiques’ 1995 313 318
[26] Cundall, A microcomputer program for modeling large-strain plasticity problems, Numerical Methods in Geomechanics pp 2101– (1988)
[27] Marti, Mixed descretization procedure for accurate modelling of plastic collapse, International Journal for Numerical and Analytical Methods in Geomechanics 6 pp 129– (1982) · Zbl 0475.73086 · doi:10.1002/nag.1610060109
[28] Tuğcu, Finite strain analysis of simple shear using recent anisotropic yield criteria, International Journal of Plasticity 10 pp 939– (1999) · Zbl 0970.74013 · doi:10.1016/S0749-6419(99)00026-1
[29] Lush, An implicit time-integration procedure for a set of internal variable constitutive equations for isotropic elasto-viscoplasticity, International Journal of Plasticity 5 pp 521– (1989) · Zbl 0695.73009 · doi:10.1016/0749-6419(89)90012-0
[30] Ortiz, Accuracy and stability of integration algorithms for elastoplastic constitutive relations, International Journal for Numerical Methods in Engineering 21 pp 1561– (1985) · Zbl 0585.73057 · doi:10.1002/nme.1620210902
[31] Hill R A theory of yielding and plastic flow of anisotropic metals 1948
[32] Braudel, An implicit incrementally objective formulation for the solution of elastoplastic problems at finite strain by the F.E.M, Computers and Structures 24 (6) pp 825– (1986) · Zbl 0604.73045 · doi:10.1016/0045-7949(86)90292-0
[33] EL Mouatassim M Modélisation en grandes transformations des solides massifs par éléments finis 1989
[34] Brunet M Modélisation numérique des grandes déformations élastoplastiques avec contact et frottement: Application à des problèmes spécifiques de la mise en forme des métaux 1987
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