On the existence of the rates of stress and displacement for Prandtl-Reuss plasticity
Author:
Gabriele Anzellotti
Journal:
Quart. Appl. Math. 41 (1983), 181-208
MSC:
Primary 73E50
DOI:
https://doi.org/10.1090/qam/719504
MathSciNet review:
719504
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- Gabriele Anzellotti and Mariano Giaquinta, Existence of the displacement field for an elastoplastic body subject to Hencky’s law and von Mises yield condition, Manuscripta Math. 32 (1980), no. 1-2, 101–136. MR 592713, DOI https://doi.org/10.1007/BF01298185
- G. Anzellotti and M. Giaquinta, On the existence of the fields of stresses and displacements for an elasto-perfectly plastic body in static equilibrium, J. Math. Pures Appl. (9) 61 (1982), no. 3, 219–244 (1983). MR 690394
- M. E. Bogovskiĭ, Solution of the first boundary value problem for an equation of continuity of an incompressible medium, Dokl. Akad. Nauk SSSR 248 (1979), no. 5, 1037–1040 (Russian). MR 553920
- G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris, 1972 (French). Travaux et Recherches Mathématiques, No. 21. MR 0464857
R. Kohn, Ph.D. Thesis, Princeton University (1979)
R. Kohn and R. Temam, to appear
- W. T. Koiter, General theorems for elastic-plastic solids, Progress in solid mechanics, Vol. 1, North-Holland Publishing Co., Amsterdam, 1960, pp. 165–221. MR 0112405
- R. Glowinski, Ervin Y. Rodin, and O. C. Zienkiewicz (eds.), Energy methods in finite element analysis, John Wiley & Sons, Ltd., Chichester, 1979. Dedicated to the memory of Professor B. Fraeijs de Veubeke; Wiley Series in Numerical Methods in Engineering; A Wiley-Interscience Publication. MR 536995
- Roger Temam and Gilbert Strang, Functions of bounded deformation, Arch. Rational Mech. Anal. 75 (1980/81), no. 1, 7–21. MR 592100, DOI https://doi.org/10.1007/BF00284617
- Pierre-M. Suquet, Evolution problems for a class of dissipative materials, Quart. Appl. Math. 38 (1980/81), no. 4, 391–414. MR 614549, DOI https://doi.org/10.1090/S0033-569X-1981-0614549-X
- R. Temam, An existence theorem for a variational problem of plasticity, Nonlinear problems of analysis in geometry and mechanics (Proc. Sympos., Univ. Paul Sabatier, Toulouse, 1979) Res. Notes in Math., vol. 46, Pitman, Boston, Mass.-London, 1981, pp. 57–70. MR 616857
G. Anzellotti and M. Giaquinta, Existence of the displacements field for an elasto-plastic body subject to Hencky’s law and Von Mises yield condition, Manuscripta Math. 32, 101–136 (1980)
G. Anzellotti and M. Giaquinta, On the existence of the fields of stresses and displacements for an elasto-perfectly plastic body in static equilibrium, 61 (1982): Journal de Mathematiques pures et appliquées
M. E. Bogovski, Solution to the first boundary value problem for the equation of continuity of an incompressible medium, Soviet Math. Dokl. 20, 1094–1098 (1979)
G. Duvaut and J. L. Lions, Les inequations en mécanique et en physique, Dunod, Paris (1972)
R. Kohn, Ph.D. Thesis, Princeton University (1979)
R. Kohn and R. Temam, to appear
W. T. Koiter, General theorems for elasto-plastic solids, in Progress in solid mechanics, 1, edited by J. N. Sneddon and R. Hill, North Holland, Amsterdam (1960)
H. Matthies, G. Strang and E. Christiansen, The saddle point of a differential program, in Energy methods in finite element analysis, edited by Glowinski, Rodin and Zienkiewicz, John Wiley and Sons (1979)
G. Strang and R. Temam, Functions of bounded deformation, Arch. Rat. Mech. Anal. 75, 7–21 (1980)
P. M. Suquet. evolution problems for a class of dissipative materials, Q. Appl. Math. 38, 391–414 (1981)
R. Temam, An existence theorem for a variational problem of plasticity, Proceedings of the Journées P. de Fermat; Atteia, Bancel, editors, Pitman (1980)
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Article copyright:
© Copyright 1983
American Mathematical Society
