The Stefan problem in a thermomechanical context with fracture and fluid flow

0579760 - ÚT 2024 RIV US eng J - Článek v odborném periodiku
Roubíček, Tomáš
The Stefan problem in a thermomechanical context with fracture and fluid flow.
Mathematical Methods in the Applied Sciences. Roč. 46, č. 12 (2023), s. 12217-12245. ISSN 0170-4214. E-ISSN 1099-1476
Grant CEP: GA ČR(CZ) GA19-04956S; GA MŠMT(CZ) EF15_003/0000493
Institucionální podpora: RVO:61388998
Klíčová slova: creep * enthalpy formulation * eulerian formulation * fully convective model * jeffreys rheology * melting * phase-field fracture * semi-compressible fluids * solid-liquid phase transition * solidification * stefan problem
Obor OECD: Applied mathematics
Impakt faktor: 2.9, rok: 2022
Způsob publikování: Omezený přístup
https://onlinelibrary.wiley.com/doi/10.1002/mma.8684

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.
Trvalý link: https://hdl.handle.net/11104/0349190