# On Ishlinskij's model for non-perfectly elastic bodies

Aplikace matematiky (1988)

- Volume: 33, Issue: 2, page 133-144
- ISSN: 0862-7940

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topKrejčí, Pavel. "On Ishlinskij's model for non-perfectly elastic bodies." Aplikace matematiky 33.2 (1988): 133-144. <http://eudml.org/doc/15530>.

@article{Krejčí1988,

abstract = {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 $u^\{\prime \prime \} + F(u)=0$ describing the motion of a mass point at the extremity of an elastico-plastic spring.},

author = {Krejčí, Pavel},

journal = {Aplikace matematiky},

keywords = {damped vibrations; asymptotic behaviour; oscillatory properties; hysteresis scheme; Ishlinskij operator; potential energies; energy inequalities; dynamic behavior; non-perfect elasticity; damped vibrations; asymptotic behaviour; oscillatory properties; hysteresis scheme; Ishlinskij operator; potential energies; energy inequalities; dynamic behavior},

language = {eng},

number = {2},

pages = {133-144},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On Ishlinskij's model for non-perfectly elastic bodies},

url = {http://eudml.org/doc/15530},

volume = {33},

year = {1988},

}

TY - JOUR

AU - Krejčí, Pavel

TI - On Ishlinskij's model for non-perfectly elastic bodies

JO - Aplikace matematiky

PY - 1988

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 33

IS - 2

SP - 133

EP - 144

AB - 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 $u^{\prime \prime } + F(u)=0$ describing the motion of a mass point at the extremity of an elastico-plastic spring.

LA - eng

KW - damped vibrations; asymptotic behaviour; oscillatory properties; hysteresis scheme; Ishlinskij operator; potential energies; energy inequalities; dynamic behavior; non-perfect elasticity; damped vibrations; asymptotic behaviour; oscillatory properties; hysteresis scheme; Ishlinskij operator; potential energies; energy inequalities; dynamic behavior

UR - http://eudml.org/doc/15530

ER -

## References

top- А.Ю. Ишлинский, Некоторые применения статистики к описанию законов деформирования тел, Изв. АН СССР, OTH, 1944, № 9, 583-590. (1944) Zbl0149.19102
- M. А. Красносельский А. В. Покровский, Системы с гистерезисом, Москва, Наука, 1983. (1983) Zbl1229.47001
- P. Krejčí, 10.1007/BF01174335, Math. Z. 193 (1986), 247-264. (193) MR0856153DOI10.1007/BF01174335
- P. Krejčí, Existence and large time behaviour of solutions to equations with hysteresis, Matematický ústav ČSAV, Praha, Preprint no. 21, 1986. (1986)

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