http://www.cnr.it/ontology/cnr/individuo/prodotto/ID31018
Phase-field models with hysteresis in one-dimensional thermo-visco-plasticity. (Articolo in rivista)
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- Phase-field models with hysteresis in one-dimensional thermo-visco-plasticity. (Articolo in rivista) (literal)
- Anno
- 2002-01-01T00:00:00+01:00 (literal)
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- Krejci P(1), Sprekels J.(2), Stefanelli U.(3) (literal)
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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)
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- ISI Web of Science (WOS) (literal)
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- (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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