Abstract
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.