WIAS Preprint No. 344, (1997)

Temperature-Dependent Hysteresis in One-Dimensional Thermovisco-Elastoplasticity


  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 35G25 73B30 73E60 73B05


  • Thermoplasticity, viscoelasticity, hysteresis, Prandtl-Ishlinskii operator, PDEs with hysteresis, thermodynamical consistency




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 σp of the form σp(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 form 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.

Appeared in

  • Appl. Math., 43 (1998), pp. 173-205

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