On Ishlinskij's model for non-perfectly elastic bodies

Pavel Krejčí

Aplikace matematiky (1988)

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

Abstract

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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.

How to cite

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Krejčí, 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

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  1. А.Ю. Ишлинский, Некоторые применения статистики к описанию законов деформирования тел, Изв. АН СССР, OTH, 1944, № 9, 583-590. (1944) Zbl0149.19102
  2. M. А. Красносельский А. В. Покровский, Системы с гистерезисом, Москва, Наука, 1983. (1983) Zbl1229.47001
  3. P. Krejčí, 10.1007/BF01174335, Math. Z. 193 (1986), 247-264. (193) Zbl0658.35065MR0856153DOI10.1007/BF01174335
  4. 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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