Geodesic
On Ishlinskij's model for non-perfectly elastic bodies
Applications of Mathematics, Tome 33 (1988) no. 2, pp. 133-144

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The main goal of the paper is to formulate some new properties of the Ishlinskii hysteresis operator $F$, which characterizes e.g. the relation between the deformation and the stress in a non-perfectly elastic (elastico-plastic) material. We introduce two energy functionals and derive the energy inequalities. As an example we investigate the equation $u'' + F(u)=0$ describing the motion of a mass point at the extremity of an elastico-plastic spring.
The main goal of the paper is to formulate some new properties of the Ishlinskii hysteresis operator $F$, which characterizes e.g. the relation between the deformation and the stress in a non-perfectly elastic (elastico-plastic) material. We introduce two energy functionals and derive the energy inequalities. As an example we investigate the equation $u'' + F(u)=0$ describing the motion of a mass point at the extremity of an elastico-plastic spring.
DOI : 10.21136/AM.1988.104294
Classification : 34A10, 34G20, 34K15, 34K25, 34K99, 46E35, 47H99, 73C50, 73E99, 74B99, 74S30
Keywords: damped vibrations; asymptotic behaviour; oscillatory properties; hysteresis scheme; Ishlinskij operator; potential energies; energy inequalities; dynamic behavior; non-perfect elasticity 
Krejčí, Pavel. On Ishlinskij's model for non-perfectly elastic bodies. Applications of Mathematics, Tome 33 (1988) no. 2, pp. 133-144. doi: 10.21136/AM.1988.104294
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[1] А.Ю. Ишлинский: Некоторые применения статистики к описанию законов деформирования тел. Изв. АН СССР, OTH, 1944, № 9, 583-590. | Zbl

[2] M. А. Красносельский А. В. Покровский: Системы с гистерезисом. Москва, Наука, 1983. | Zbl

[3] P. Krejčí: Hysteresis and periodic solutions of semilinear and quasilinear wave equations. Math. Z. 193 (1986), 247-264. | DOI | MR

[4] P. Krejčí: Existence and large time behaviour of solutions to equations with hysteresis. Matematický ústav ČSAV, Praha, Preprint no. 21, 1986.

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