Duality preserving discretization of the large time increment methods. (English) Zbl 0983.74081

From the summary: We present an alternative to the classical large time increment method: space and time discretizations which preserve the duality structure of continuous problems are introduced first, then the method is reformulated for discrete problems. It is shown how the so-called ‘generalized variable’ modelling preserves the fundamental duality structure of continuum problems. A proof of convergence of iterative scheme to the solution of the discrete problem is also outlined.


74S30 Other numerical methods in solid mechanics (MSC2010)
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
Full Text: DOI


[1] Ladevèze, P., Sur une famille d’algorithmes en méchanique des structures, Compte rendus acad. sc. Paris, 300II, 41-44, (1985) · Zbl 0597.73089
[2] Rice, J.R., Inelastic constitutive relations for solids, an internal variable theory and its application to metal plasticity, J. mech. phys. solids, 9, 433-455, (1971) · Zbl 0235.73002
[3] J.J. Moreau, On unilateral constraints, friction and plasticity, in: G. Capriz and G. Stampacchia (Eds.), New Variational Techniques in Mathematical Physics, Cremonese, Italia, 1974, pp. 175-322
[4] Watanabe, O.; Atluri, S.N., Internal time, general internal variable and multi-yield-surface theories of plasticity and creep: a unification of concepts, Int. J. plasticity, 2, 37-57, (1986) · Zbl 0618.73038
[5] Halphen, B.; Nguyen, Q.S., Sur le matériaux standards generalisés, J. de mech., 14, 39-63, (1975) · Zbl 0308.73017
[6] G. Cailleteau, P. Pilvin, Identification and inverse problems related to material behavior, in: H.D. Bui et al. (Eds.), Inverse Problems in Engineering Mechanics, Balkema, Rotterdam, 1994, pp. 79-86
[7] Chaboche, J.L., Cyclic viscoplasticity constitutive equations, J. appl. mech., 60, 813-828, (1993) · Zbl 0816.73014
[8] J. Lemaitre, J.L. Chaboche, Mechanics of Solid Materials, Cambridge, 1990 · Zbl 0743.73002
[9] Herakovich, C.T., Mechanics of fibrous composites, (1998), Wiley London · Zbl 0606.73091
[10] P. Ladevèze, New advances in the large time increment method, in: P. Ladevéze, O.C. Zienkiewicz (Eds.), New Advances in Computational Structural Mechanics, Elsevier, Amsterdam, 1991, pp. 3-21
[11] P. Ladevèze, Nonlinear Computational Structural Mechanics, Springer, New York, 1998, French edition Hermes, Paris, 1996
[12] Cognard, J.Y.; Ladevèze, P., A large time increment approach for cyclic plasticity, Int. J. plasticity, 9, 114-157, (1993) · Zbl 0772.73028
[13] Blanze, C.; Champaney, L.; Cognard, J.Y.; Ladevèze, P., A modular approach for structure assembly computations. application to contact problems, Engrg. comput., 13, 15-32, (1996)
[14] Boucard, P.A.; Ladevèze, P.; Poss, M.; Rougee, P., A non-incremental approach for large displacement problems, Comput. struct., 64, 499-508, (1997) · Zbl 0919.73167
[15] Champaney, L.; Cognard, J.Y.; Dureisseix, D.; Ladevèze, P., Large scale application on parallel computers of mixed domain decomposition methods, Comput. mech., 19, 253-263, (1997) · Zbl 0894.73211
[16] P. Ladevèze, J.Y. Cognard, P. Talbot, A non-incremental and adaptive computational approach in thermo-viscoplasticity, in: O.T. Bruhns, E. Stein (Eds.), Micro and Macro-Structural Aspects of Thermoplasticity, Springer, Berlin, 1998 (to appear)
[17] J.H. Argyris, Continua and discontinua, in: Proceedings of the First Conference on Matrix Methods in Structural Mechanics, Dayton, 1966, pp. 66-88
[18] Maier, G., Quadratic programming and theory of elastic-perfectly plastic structures, Meccanica, 3, 1-9, (1968)
[19] Corradi, L., On compatible finite element models for elastic – plastic analysis, Meccanica, 13, 133-150, (1978) · Zbl 0417.73073
[20] Corradi, L., A displacement formulation for the finite element elastic – plastic problem, Meccanica, 18, 77-91, (1983) · Zbl 0519.73072
[21] Corradi, L., On stress computation in displacement finite element models, Comput. meth. appl. mech. engrg., 54, 325-339, (1986) · Zbl 0566.73057
[22] Comi, C.; Maier, G.; Perego, U., Generalized variable finite element modelling and extremum theorems in stepwise holonomic elastoplasticity with internal variables, Comput. meth. appl. mech. engrg., 96, 213-237, (1992) · Zbl 0761.73107
[23] Comi, C.; Perego, U., A unified approach for variationally consistent finite elements in elastoplasticity, Comput. meth. appl. mech. engrg., 121, 323-344, (1995) · Zbl 0852.73058
[24] Simo, J.C.; Govindjee, S., Nonlinear B-stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity, Int. J. numer. meth. engrg., 31, 151-176, (1990) · Zbl 0825.73959
[25] Corigliano, A.; Perego, U., Generalized mid-point finite element dynamic analysis of elastoplastic systems, Int. J. numer. meth. engrg., 36, 361-383, (1993) · Zbl 0769.73076
[26] DeSaxcé, G., A generalization of Fenchel’s inequality and its applications to the constitutive law, C. R. acad sci. Paris, 314, II, 125-129, (1992)
[27] Berga, A.; De Saxcé, G., Elastoplastic finite element analysis of soil problems with implicit standard material constitutive law, Rev. eur. elem. finis, 3, 411-436, (1994) · Zbl 0924.73258
[28] W. Prager, The general theory of limit design, in: Proceedings of the Eighth International Conference on Applied Mechanics, 2, Instanbul, 1952, pp. 65-72
[29] Capurso, M.; Maier, G., Incremental elastoplastic analysis and quadratic optimization, Meccanica, 2, 107-116, (1970) · Zbl 0198.58301
[30] Simo, J.C.; Kennedy, J.C.; Taylor, R.L., Complementary mixed finite element formulations for elastoplasticity, Comput. meth. appl. mech. engrg., 74, 177-206, (1989) · Zbl 0687.73064
[31] Zienkiewicz, O.C.; Taylor, R.L., The finite element method, (1989), Mc Graw-Hill New York · Zbl 0991.74002
[32] Stolarski, H.; Belytschko, T., Limitation principles for mixed finite elements based on the hu-washizu variational formulation, Comput. meth. appl. mech. engrg., 60, 195-216, (1987) · Zbl 0613.73017
[33] Comi, C.; Perego, U., A generalized variable formulation for gradient dependent softening plasticity, Int. J. numer. meth. engrg., 39, 3731-3755, (1996) · Zbl 0894.73149
[34] C. Polizzotto, G. Borino, P. Fuschi, A finite interval approach to evolutive elastic – plastic analysis, in: P. Ladeveze, O.C. Zienkiewicz (Eds.), New Advances in Computational Structural Mechanics, Elsevier, Amsterdam, 1991, pp. 23-37
[35] P. Ladevèze, J.T. Oden (Eds.), Advances in Adaptive Computational Methods, Elsevier, Amsterdam, 1997
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.