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Mathematical models of hysteresis. (English) Zbl 0656.73043

Topics in nonsmooth mechanics, 295-326 (1988).
[For the entire collection see Zbl 0646.00014.]
Hysteretic effects are considered here with the help of Volterra-like functionals, i.e. functionals depending on the past history. The classical Duhem-Madelung and Preisach models of hysteresis are introduced. Following the work of Krasnosel’skij, existence theorems are presented for some examples ranging from ferromagnetism, biological models and plasticity to surface tension at solid liquid interfaces.
Reviewer: H.Matthies

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74S99 Numerical and other methods in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74L15 Biomechanical solid mechanics
74A15 Thermodynamics in solid mechanics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
47A53 (Semi-) Fredholm operators; index theories