×

Study of an elastoplastic model with an infinite number of internal degrees of freedom. (English) Zbl 1023.74009

Summary: We examine the dynamical behavior of continuous elastoplastic Masing model consisting of an infinite number of springs and dry-friction elements. Using the theory of differential inclusions, we prove existence and uniqueness result. Moreover, we prove that the continuous model is the limit of discrete Masing model when the number of degrees of freedom tends to infinity. Starting from known numerical results, we construct an implicit Euler-like numerical scheme of order one.

MSC:

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

References:

[1] Alber, H.-D., Materials with Memory. Materials with Memory, Lecture Notes in Mathematics, 1682 (1998), Springer-Verlag: Springer-Verlag Berlin · Zbl 0977.35001
[2] Bastien, J., 2000. Étude théorique et numérique d’inclusions différentielles maximales monotones. Applications à des modèles élastoplastiques. PhD thesis, Université Lyon I, No. 96-2000; Bastien, J., 2000. Étude théorique et numérique d’inclusions différentielles maximales monotones. Applications à des modèles élastoplastiques. PhD thesis, Université Lyon I, No. 96-2000
[3] Bastien, J., Schatzman, M., 1999. Précision de schémas numériques en évolution multivoque. Preprint 307. Available on http://numerix.univ-lyon1.fr/publis/publiv/1999/publis.html; Bastien, J., Schatzman, M., 1999. Précision de schémas numériques en évolution multivoque. Preprint 307. Available on http://numerix.univ-lyon1.fr/publis/publiv/1999/publis.html
[4] Bastien, J.; Schatzman, M., Schéma numérique pour des inclusions différentielles avec terme maximal monotone, C. R. Acad. Sci. Paris Sér. I Math., 330, 611-615 (2000) · Zbl 0951.65059
[5] Bastien, J.; Schatzman, M.; Lamarque, C.-H., Study of some rheological models with a finite number of degrees of freedom, Eur. J. Mech. A Solids, 19, 2, 277-307 (2000) · Zbl 0954.74011
[6] Brezis, H., Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert. Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Mathematics Studies, 5 (1973), North-Holland: North-Holland Amsterdam, Notas de Matemática (50) · Zbl 0252.47055
[7] Deimling, K., Multivalued Differential Equations (1992), de Gruyter: de Gruyter Berlin · Zbl 0760.34002
[8] Fougères, R.; Sidoroff, F., The evolutive masing model and its application to cyclic plasticity and ageing, Nuclear Engineering and Design, 114, 273-284 (1989)
[9] Hlavácheck, I.; Haslinger, J.; Necheckcas, J.; Lovícheck, Solution of Variational Inequalities in Mechanics (1988), Springer-Verlag: Springer-Verlag New York · Zbl 0654.73019
[10] Hu, S.; Papageorgiou, N. S., Time-dependent subdifferential evolution inclusions and optimal control, Mem. Amer. Math. Soc., 133, 632 (1998) · Zbl 0909.49005
[11] Lippold, G., Error estimates for the implicit Euler approximation of an evolution inequality, Nonlinear Anal., 15, 11, 1077-1089 (1990) · Zbl 0727.65058
[12] Monteiro Marques, M. D.P., Differential Inclusions in Nonsmooth Mechanical Problems. Shocks and Dry Friction (1993), Birkhäuser: Birkhäuser Basel · Zbl 0802.73003
[13] Moreau, J. J., Unilateral contact and dry friction in finite freedom dynamics, (Moreau, J. J.; Panagiotopoulos, P. D., Nonsmooth Mechanics and Applications (1988), Springer-Verlag), 1-81 · Zbl 0703.73070
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.