Convex Analysis, Maximal Monotone Operators, and Elasto-Viscoplastic Material with Linear Hardening and Hysteresis

  • Eberhard Zeidler


In this chapter we generalize the results of Chapter 60 about the wire to three-dimensional bodies.


Abstract Model Convex Analysis Inverse Operator Plasticity Theory Maximal Monotone Operator 
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References to the Literature

  1. Internal state variables: Nguyen (1973), Gröger (1979, S, B) (general abstract model). Hünlich (1979) (plastic torsion), Necas and Hlavácek (1981, M).Google Scholar
  2. Classical works in plasticity theory: See the References to the Literature for Chapter 60.Google Scholar
  3. Textbooks on classical plasticity theory: Hill (1950, M), Prager and Hodge (1951, M, H), Prager (1955, M), Sokolovskii (1955, M), Kacanov (1969, M).Google Scholar
  4. Handbook of Physics: Flügge (1956), Vol. Via, Part 3, Geiringer (1972, S).Google Scholar
  5. Explicit examples in plasticity theory: Nguyen (1982, L).Google Scholar
  6. Modern introduction to plasticity theory: Duvaut and Lions (1972, M), Gröger (1979, S, B), Necas and Hlavácek (1981, M), Temam (1983a, M).Google Scholar
  7. Existence proofs: Duvaut and Lions (1972, M), Nguyen (1973), Halphen and Nguyen (1975), Moreau (1976), Gröger (1979), Miersemann (1980) (regularity of generalized solutions), Neöas and Hlavácek (1981, M), Temam (1983a, M), (1986).Google Scholar
  8. General systems with hysteresis: Krasnoselskii and Pokrovskii (1983, M).Google Scholar
  9. Classical plastic torsion: Prager and Hodge (1951, M), Geiringer (1972, S).Google Scholar
  10. Modem plastic torsion: Duvaut and Lions (1972, M), Lanchon (1974), and Friedman (1982, M) (introduction).Google Scholar
  11. Ting (1969), (1972, S), Gajewski (1970a), Brézis (1972), Langenbach (1976, M), Gerhardt (1976), Hünlich (1979), Glowinski (1980, L).Google Scholar
  12. Approximation methods: Glowinski, Lions, and Trémoliéres (1976, M), Hünlich (1979), Glowinski (1980, L), (1984, M), Korneev and Lange (1984, L), Miyoshi (1985, M).Google Scholar
  13. Plasticity, defects in crystals, and the methods of the modern gauge field theory: Kleinert (1987, P).Google Scholar

Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Eberhard Zeidler
    • 1
  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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