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The Stefan problem in a thermomechanical context with fracture and fluid flow
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SYSNO ASEP 0579760 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The Stefan problem in a thermomechanical context with fracture and fluid flow Author(s) Roubíček, Tomáš (UT-L) RID, ORCID Number of authors 1 Source Title Mathematical Methods in the Applied Sciences. - : Wiley - ISSN 0170-4214
Roč. 46, č. 12 (2023), s. 12217-12245Number of pages 29 s. Publication form Print - P Language eng - English Country US - United States Keywords creep ; enthalpy formulation ; eulerian formulation ; fully convective model ; jeffreys rheology ; melting ; phase-field fracture ; semi-compressible fluids ; solid-liquid phase transition ; solidification ; stefan problem OECD category Applied mathematics Subject RIV - cooperation General Mathematics R&D Projects GA19-04956S GA ČR - Czech Science Foundation (CSF) EF15_003/0000493 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Method of publishing Limited access Institutional support UT-L - RVO:61388998 UT WOS 000967855900001 EID SCOPUS 85152357611 DOI 10.1002/mma.8684 Annotation The classical Stefan problem, concerning mere heat-transfer during solid-liquid phase transition, is here enhanced towards mechanical effects. The Eulerian description at large displacements is used with convective and Zaremba-Jaumann corotational time derivatives, linearized by using the additive Green-Naghdi's decomposition in (objective) rates. In particular, the liquid phase is a viscoelastic fluid while creep and rupture of the solid phase is considered in the Jeffreys viscoelastic rheology exploiting the phase-field model and a concept of slightly (so-called semi) compressible materials. The L-1-theory for the heat equation is adopted for the Stefan problem relaxed by allowing for kinetic superheating/supercooling effects during the solid-liquid phase transition. A rigorous proof of existence of weak solutions is provided for an incomplete melting, employing a time discretization approximation. Workplace Institute of Thermomechanics Contact Marie Kajprová, kajprova@it.cas.cz, Tel.: 266 053 154 ; Jana Lahovská, jaja@it.cas.cz, Tel.: 266 053 823 Year of Publishing 2024 Electronic address https://onlinelibrary.wiley.com/doi/10.1002/mma.8684
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