Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity

Pavel Krejčí; Jürgen Sprekels

Applications of Mathematics (1998)

  • Volume: 43, Issue: 3, page 173-205
  • ISSN: 0862-7940

Abstract

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In this paper, we develop a thermodynamically consistent description of the uniaxial behavior of thermovisco-elastoplastic materials for which the total stress σ contains, in addition to elastic, viscous and thermic contributions, a plastic component σ p of the form σ p ( x , t ) = 𝒫 [ ε , θ ( x , t ) ] ( x , t ) . Here ε and θ are the fields of strain and absolute temperature, respectively, and { 𝒫 [ · , θ ] } θ > 0 denotes a family of (rate-independent) hysteresis operators of Prandtl-Ishlinskii type, parametrized by the absolute temperature. The system of momentum and energy balance equations governing the space-time evolution of the material forms a system of two highly nonlinearly coupled partial differential equations involving partial derivatives of hysteretic nonlinearities at different places. It is shown that an initial-boundary value problem for this system admits a unique global strong solution which depends continuously on the data.

How to cite

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Krejčí, Pavel, and Sprekels, Jürgen. "Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity." Applications of Mathematics 43.3 (1998): 173-205. <http://eudml.org/doc/33006>.

@article{Krejčí1998,
abstract = {In this paper, we develop a thermodynamically consistent description of the uniaxial behavior of thermovisco-elastoplastic materials for which the total stress $\sigma $ contains, in addition to elastic, viscous and thermic contributions, a plastic component $\sigma ^p$ of the form $\sigma ^p(x,t)=\{\mathcal \{P\}\}[\varepsilon ,\theta (x,t)](x,t)$. Here $\varepsilon $ and $\theta $ are the fields of strain and absolute temperature, respectively, and $\lbrace \{\mathcal \{P\}\}[\cdot ,\theta ]\rbrace _\{\theta > 0\}$ denotes a family of (rate-independent) hysteresis operators of Prandtl-Ishlinskii type, parametrized by the absolute temperature. The system of momentum and energy balance equations governing the space-time evolution of the material forms a system of two highly nonlinearly coupled partial differential equations involving partial derivatives of hysteretic nonlinearities at different places. It is shown that an initial-boundary value problem for this system admits a unique global strong solution which depends continuously on the data.},
author = {Krejčí, Pavel, Sprekels, Jürgen},
journal = {Applications of Mathematics},
keywords = {thermoplasticity; viscoelasticity; hysteresis; Prandtl-Ishlinskii operator; PDEs with hysteresis; thermodynamical consistency; thermoplasticity; viscoelasticity; hysteresis; Prandtl-Ishlinskii operator; PDEs with hysteresis; thermodynamical consistency; unique global strong solution},
language = {eng},
number = {3},
pages = {173-205},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity},
url = {http://eudml.org/doc/33006},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Krejčí, Pavel
AU - Sprekels, Jürgen
TI - Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 3
SP - 173
EP - 205
AB - In this paper, we develop a thermodynamically consistent description of the uniaxial behavior of thermovisco-elastoplastic materials for which the total stress $\sigma $ contains, in addition to elastic, viscous and thermic contributions, a plastic component $\sigma ^p$ of the form $\sigma ^p(x,t)={\mathcal {P}}[\varepsilon ,\theta (x,t)](x,t)$. Here $\varepsilon $ and $\theta $ are the fields of strain and absolute temperature, respectively, and $\lbrace {\mathcal {P}}[\cdot ,\theta ]\rbrace _{\theta > 0}$ denotes a family of (rate-independent) hysteresis operators of Prandtl-Ishlinskii type, parametrized by the absolute temperature. The system of momentum and energy balance equations governing the space-time evolution of the material forms a system of two highly nonlinearly coupled partial differential equations involving partial derivatives of hysteretic nonlinearities at different places. It is shown that an initial-boundary value problem for this system admits a unique global strong solution which depends continuously on the data.
LA - eng
KW - thermoplasticity; viscoelasticity; hysteresis; Prandtl-Ishlinskii operator; PDEs with hysteresis; thermodynamical consistency; thermoplasticity; viscoelasticity; hysteresis; Prandtl-Ishlinskii operator; PDEs with hysteresis; thermodynamical consistency; unique global strong solution
UR - http://eudml.org/doc/33006
ER -

References

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