Geodesic
Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity
Applications of Mathematics, Tome 43 (1998) no. 3, pp. 173-205

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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 $\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.
DOI : 10.1023/A:1023224507448
Classification : 35G25, 73B05, 73B30, 73E60, 74N30
Keywords: thermoplasticity; viscoelasticity; hysteresis; Prandtl-Ishlinskii operator; PDEs with hysteresis; thermodynamical consistency 
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     title = {Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity},
     journal = {Applications of Mathematics},
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Krejčí, Pavel; Sprekels, Jürgen. Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity. Applications of Mathematics, Tome 43 (1998) no. 3, pp. 173-205. doi: 10.1023/A:1023224507448

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