Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. (English) Zbl 0764.73089


74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20 Large-strain, rate-dependent theories of plasticity
74C99 Plastic materials, materials of stress-rate and internal-variable type


Full Text: DOI


[1] Hill, R., The Mathematical Theory of Plasticity (1950), Clarendon: Clarendon Oxford · Zbl 0041.10802
[2] Koiter, W. T., General theorems for elastic-plastic solids, Prog. Solid Mech., 1, 167-221 (1960)
[3] Duvaut, G.; Lions, J. L., Les Inequations en Mechanique et en Physique (1972), Dunot: Dunot Paris · Zbl 0298.73001
[4] Johnson, C., On plasticity with hardening, J. Appl. Math. Anal., 62, 325-336 (1978) · Zbl 0373.73049
[5] Matthies, H., Existence theorems in thermo-plasticity, J. Mech., 18, 695-711 (1979)
[6] Suquet, P., Sur les equations de la plasticite, Ann. Fac. Sciences Toulouse, 1, 77-87 (1979) · Zbl 0405.46027
[7] Temam, R.; Strang, G., Functions of bounded deformation, Arch. Rational Mech. Anal., 75, 7-21 (1980) · Zbl 0472.73031
[8] Moreau, J. J., Evolution problem associated with a moving convex set in a Hilbert space, J. Differential Equations, 26, 347 (1977) · Zbl 0356.34067
[9] Wilkins, M. L., Calculation of elastic-plastic flow, (Alder, B.; Fernback, S.; Rotenberg, M., Methods of Computational Physics, Vol. 3 (1964), Academic Press: Academic Press New York), 211-272
[10] Maenchen, G.; Sacks, S., The tensor code, (Alder, B.; Fernback, S.; Rotenberg, M., Methods of Computational Physics, Vol. 3 (1964), Academic Press: Academic Press New York), 181-210
[11] Burrage, K.; Butcher, J. C., Nonlinear stability of a general class of differential equation methods, BIT 20, 185-203 (1980) · Zbl 0431.65051
[12] Simo, J. C., Nonlinear stability of the time-discrete variational problem of evolution in nonlinear heat conduction, plasticity and elastoplasticity, Comput. Methods Appl. Mech. Engrg., 88, 111-131 (1991) · Zbl 0751.73066
[13] Strang, H.; Matthies, H.; Temam, R., Mathematical and computational methods in plasticity, (Nemat-Nasser, S., Variational Methods in the Mechanics of Solids, Vol. 3 (1980), Pergamon: Pergamon Oxford)
[14] Simo, J. C.; Taylor, R. L., Consistent tangent operators for rate-independent elastoplasticity, Comput. Methods Appl. Mech. Engrg., 48, 101-118 (1985) · Zbl 0535.73025
[15] Ogden, R. W., Nonlinear Elastic Deformations (1984), Ellis Harwood: Ellis Harwood Chichester · Zbl 0541.73044
[16] Lee, E. H., Elastic-plastic deformation at finite strains, J. Appl. Mech., 1-6 (1969) · Zbl 0179.55603
[17] Mandel, J., Thermodynamics and plasticity, (Delgado Domingers, J. J.; Nina, N. R.; Whitelaw, J. H., Foundations of Continuum Thermodynamics (1974), Macmillan: Macmillan London), 283-304
[18] Needleman, A.; Tvergaard, V., Finite element analysis of localization plasticity, (Oden, J. T.; Carey, G. F., Finite Elements, Vol. V: Special Problems in Solid Mechanics (1984), Prentice Hall: Prentice Hall Englewood Cliffs, NJ) · Zbl 0942.74620
[19] Hughes, T. J.R., Numerical implementation of constitutive models: Rate independent deviatoric plasticity, (Nemat-Nasser, S.; Asaro, R.; Hegemier, G., Theoretical Foundations for Large Scale Computations of Nonlinear Material Behaviour (1984), Martinus Nijhoff: Martinus Nijhoff The Netherlands)
[20] Argyris, J. H.; Doltsinis, J. St., On the large strain inelastic analysis in natural formulation — Part I: Quasistatic problems, Comput. Methods Appl. Mech. Engrg., 20, 213-252 (1979) · Zbl 0437.73065
[21] Argyris, J. H.; Doltsinis, J. St.; Pimenta, P. M.; Wüstenberg, H., Thermomechanical response of solids at high strains - natural approach, Comput. Methods Appl. Mech. Engrg., 32, 3-57 (1982) · Zbl 0505.73062
[22] Simo, J. C.; Ortiz, M., A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations, Comput. Methods Appl. Mech. Engrg., 49, 221-245 (1985) · Zbl 0566.73035
[23] Simo, J. C., On the computational significance of the intermediate configuration and hyperelastic stress relations in finite deformation elastoplasticity, Mech. Mater., 4, 439-451 (1985)
[24] Nagtegaal, J. C.; Parks, D. M.; Rice, J. R., On numerically accurate finite element solutions in the fully plastic range, Comput. Methods Appl. Mech. Engrg., 4, 153-177 (1974) · Zbl 0284.73048
[25] Simo, J. C.; Taylor, R. L.; Pister, K. S., Variational and projection methods for the volume constraint in finite deformation elasto-plasticity, Comput. Methods Appl. Mech. Engrg., 51, 177-208 (1985) · Zbl 0554.73036
[26] Simo, J. C., A framework for finite strain elastoplasticity based on maximum plastic dissipation and multiplicative decomposition: Part I. Continuum formulation; Part II. Computational aspects, Comput. Methods Appl. Mech. Engrg., 68, 1-31 (1988) · Zbl 0644.73043
[27] Weber, G.; Anand, L., Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoelastic solids, Comput. Methods Appl. Mech. Engrg., 79, 173-202 (1990) · Zbl 0731.73031
[28] Eterovich, A. L.; Bathe, K. J., A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using logarithmic stresses and strain measures, Internat. J. Numer. Methods Engrg., 30, 1099-1115 (1990) · Zbl 0714.73035
[29] Rolph, W. D.; Bathe, K. J., On a large strain finite element formulation for elastoplastic analysis, (Willan, K. J., Constitutive Equations: Macro and Computational Aspects, Winter Annual Meeting (1984), ASME: ASME New York), 131-147
[30] Peric, Dj.; Owen, D. R.J.; Honnor, M. E., A model for finite strain elastoplasticity, (Owen, R.; Hinton, E.; Onate, E., Proc. 2nd Internat. Conf. on Computational Plasticity (1989), Pineridge: Pineridge Swansea), 111-126
[31] Moran, B.; Ortiz, M.; Shi, F., Formulation of implicit finite element methods for multiplicative plasticity, Internat. J. Numer. Methods Engrg., 29, 483-514 (1990) · Zbl 0724.73221
[33] Kim, S. J.; Oden, J. T., Finite element analysis of a class of problems in finite strain elastoplasticity based on the thermodynamical theory of materials of type N, Comput. Methods Appl. Mech. Engrg., 53, 277-302 (1985) · Zbl 0552.73066
[34] Simo, J. C.; Miehe, C., Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation, Comput. Methods Appl. Mech. Engrg., 98, 41-104 (1992) · Zbl 0764.73088
[35] Truesdell, C.; Noll, W., The nonlinear field theories of mechanics, (Fluegge, S., Handbuch der Physik, Bd. III/3 (1965), Springer: Springer Berlin) · Zbl 0779.73004
[36] Simo, J. C.; Tarnow, N.; Wong, K. K., Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics, Comput. Methods Appl. Mech. Engrg. (1992), to appear · Zbl 0764.73096
[37] Asaro, R., Micromechanics of crystals and polycrystals, Adv. Appl. Mech., 23, 1-115 (1983)
[38] Kato, T., On the Trotter-Lie product formula, (Proc. Japan Acad., 50 (1974)), 694-698 · Zbl 0336.47018
[39] Yanenko, N. N., The Method of Fractional Steps (1971), Springer: Springer Berlin · Zbl 0209.47103
[40] Marchuck, G. I.; Shaidurov, V. V., Difference Methods and their Extrapolation (1983), Springer: Springer New-York
[41] Richtmyer, R. D.; Morton, K. W., Difference Methods for Initial Value Problems (1967), Interscience: Interscience New York · Zbl 0155.47502
[42] Krieg, R. D.; Krieg, D. B., Accuracies of numerical solution methods for the elastic-perfectly plastic models, ASME J. Pressure Vessel Technol., 99 (1977)
[43] Simo, J. C.; Taylor, R. L., A return mapping algorithm for plane stress elastoplasticity, Internat. J. Numer. Methods Engrg., 22, 649-670 (1986) · Zbl 0585.73059
[44] Simo, J. C.; Taylor, R. L., Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms, Comput. Methods Appl. Mech. Engrg., 85, 273-310 (1991) · Zbl 0764.73104
[45] Simo, J. C.; Kennedy, J. G.; Govindjee, S., General return mapping algorithms for multisurface plasticity and viscoplasticity, Internat. J. Numer. Methods Engrg., 26, 2161-2185 (1988) · Zbl 0661.73058
[46] Ciarlet, P. G., The Finite Element Method for Elliptic Problems (1978), North-Holland: North-Holland Amsterdam · Zbl 0445.73043
[47] Krieg, R. D.; Key, S. W., Implementation of a time dependent plasticity theory into structural computer programs, (Stricklin, J. A.; Saczlski, K. J., Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects, AMD-20 (1976), ASME: ASME New York) · Zbl 0471.73077
[48] Brezzi, F.; Fortin, M., Mixed and Hybrid Finite Element Methods (1990), Springer: Springer Berlin · Zbl 1009.65067
[49] Scott, L. R.; Vogelius, M., Conforming finite element methods for incompressible and nearly incompressible continua, Lectures Appl. Math., 22, 221-244 (1985) · Zbl 0582.76028
[50] Simo, J. C.; Rifai, A class of mixed assumed strain methods and the method of incompatible modes, Internat. J. Numer. Methods Engrg., 29, 1595-1638 (1990) · Zbl 0724.73222
[51] Hughes, T. J.R., Generalization of selective integration procedures to anistropic and nonlinear media, Internat. J. Numer. Methods Engrg., 15, 1413-1418 (1980) · Zbl 0437.73053
[52] Sussman, T.; Bathe, K. J., A finite element formulation for nonlinear incompressible elastic and inelastic analysis, Comput. & Structures, 26, 109-357 (1987) · Zbl 0609.73073
[53] Taylor, R. L.; Beresford, P. J.; Wilson, E. L., A non-conforming element for stress analysis, Internat. J. Numer. Methods Engrg., 10, 1211-1219 (1976) · Zbl 0338.73041
[55] Wanner, G., A short proof of nonlinear A-stability, BIT 16, 226-227 (1965) · Zbl 0329.65048
[56] Hilber, H. M.; Hughes, T. J.R.; Taylor, R. L., Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Engrg. Struct. Dynam., 5, 283-292 (1977)
[57] Miranda, I.; Ferencz, R. M.; Hughes, T. J.R., An improved implicit-explicit time integration method for structural dynamics, Earthquake Engrg. Struct. Dynam., 18, 643-653 (1989)
[58] Hilber, H. M., Analysis and design of numerical integration methods in structural dynamics, (Report No. E.E.R.C. 76-29 (1976), Earthquake Eng. Research Center, University of California: Earthquake Eng. Research Center, University of California Berkeley, CA)
[59] Rice, J. R.; Tracey, D. M., Computational fracture mechanics, (Fenves, S. J., Proc. Symp. on Numerical Methods in Structural Mechanics (1973), Academic Press: Academic Press Urbana, IL)
[60] Hughes, T. J.R.; Taylor, R. L., Unconditionally stable algorithms for quasi-static elasto/viscoplastic finite element analysis, Comput. & Structures, 8, 169-173 (1978) · Zbl 0365.73029
[61] Ortiz, M.; Popov, E. P., Accuracy and stability of integration algorithms for elastoplastic constitutive relations, Internat. J. Numer. Methods Engrg., 21, 1561-1576 (1985) · Zbl 0585.73057
[62] Zienkiewicz, O. C.; Taylor, R. L., (The Finite Element Method, Vol. 1 (1989), McGraw-Hill: McGraw-Hill London)
[63] Hallquist, J. O.; Benson, D. J., (DYNA3D User’s Manual (1987), Lawrence Livermore National Laboratory), Report No. UCID-19592, Rev. 3
[64] Nagtegaal, J. C.; de Jong, J. E., Some aspects of non-isotropic work-hardening in finite strain plasticity, (Lee, E. H.; Mallet, R. L., Plasticity of Metals at Finite Strains, Proc. Research Workshop (1981), Stanford University), 65-102
[65] Ciarlet, P. G., Three-dimensional Mathematical Elasticity (1981), North-Holland: North-Holland Amsterdam · Zbl 0489.73057
[66] Coleman, B. D.; Gurtin, M. E., Thermodynamics with internal state variables, J. Chem. Phys., 47, 597-613 (1967)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.