Mathematical models of hysteresis. (English) Zbl 0656.73043

Visintin, A.

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

Keywords:

Volterra-like functionals; Duhem-Madelung and Preisach models; existence theorems

Citations:

Zbl 0575.35045; Zbl 0608.65082; Zbl 0573.34016; Zbl 0576.35103; Zbl 0646.00014