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The Stefan problem in a thermomechanical context with fracture and fluid flow
  • Tomáš Roubíček
Tomáš Roubíček
Charles University

Corresponding Author:[email protected]

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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 exploiting 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, exploiting 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 week solutions is provided for an incomplete melting, exploiting a time-discretisation approximation.
19 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
21 Nov 2021Submission Checks Completed
21 Nov 2021Assigned to Editor
03 Dec 2021Reviewer(s) Assigned
02 Aug 2022Review(s) Completed, Editorial Evaluation Pending
03 Aug 2022Editorial Decision: Revise Minor
15 Aug 20221st Revision Received
17 Aug 2022Submission Checks Completed
17 Aug 2022Assigned to Editor
17 Aug 2022Reviewer(s) Assigned
18 Aug 2022Review(s) Completed, Editorial Evaluation Pending
18 Aug 2022Editorial Decision: Accept