Phase-field models with hysteresis in one-dimensional thermo-visco-plasticity. (Articolo in rivista)

Type
Label
  • Phase-field models with hysteresis in one-dimensional thermo-visco-plasticity. (Articolo in rivista) (literal)
Anno
  • 2002-01-01T00:00:00+01:00 (literal)
Alternative label
  • Krejci P(1), Sprekels J.(2), Stefanelli U.(3) (2002)
    Phase-field models with hysteresis in one-dimensional thermo-visco-plasticity.
    in SIAM journal on mathematical analysis (Print)
    (literal)
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  • Krejci P(1), Sprekels J.(2), Stefanelli U.(3) (literal)
Pagina inizio
  • 409 (literal)
Pagina fine
  • 434 (literal)
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  • CIT articolo = 2 ; Impact Factor rivista: 0.909 (literal)
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  • 34 (literal)
Rivista
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  • The fully coupled macroscopic thermo-mechanical behavior of standard materials is generally quite complex. Indeed, thermal, visco-elastic, and phase-changing phenomena are to be considered at once. The latter often give rise to complex dynamics, possibly including various hysteresis effects. In this paper we focus on the possibility of introducing some hysteresis behavior directly in the model by establishing some of the constitutive relations to be of hysteretic type. The strongly nonlinear system of PDE's that arises within this framework is proved to be suitably well-posed in the one-dimensional setting. A second contribution in this same direction is the paper [P. Krejci, J. Sprekels, and U. Stefanelli, One-dimensional thermo-visco-plastic processes with hysteresis and phase transitions, Adv. Math. Sci. Appl., 13, 2:695-712, 2003]. (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • (1) Acad. Sci. Czech Republ., Prague, Czech Republic; (2) Weierstrass Inst. Appl. Anal. & Stochast., Berlin; (3) IMATI-CNR (literal)
Titolo
  • Phase-field models with hysteresis in one-dimensional thermo-visco-plasticity. (literal)
Abstract
  • This paper introduces a combined one-dimensional model for thermoviscoplastic behavior under solid-solid phase transformations that incorporates the occurrence of hysteresis effects in both the strain-stress law and the phase transition described by the evolution of a phase-field (which is usually closely related to an order parameter of the phase transition). Hysteresis is accounted for using the mathematical theory of hysteresis operators developed in the past thirty years. The model extends recent works of the first two authors on phase-field models with hysteresis to the case when mechanical effects can no longer be ignored or even prevail. It leads to a strongly nonlinear coupled system of partial differential equations in which hysteresis nonlinearities occur at several places, even under time and space derivatives. We show the thermodynamic consistency of the model, and we prove its well-posedness. (literal)
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