Abstract: We propose to model the occurrence of high stresses
in an elastic or elastoplastic bottle of water subject to freezing.
The process is described by a system of three evolution
equations for temperature (energy balance), volume
(momentum balance), and liquid fraction (phase relaxation law).
Due to high pressure, the freezing temperature inside the bottle
is lower than the one at normal pressure. If in this situation the
bottle breaks, an instantaneous solidification takes place.
We derive a formula for the undercooling rate in terms of the
elasticity moduli. If the bottle is elastoplastic, we observe a
permanent deformation after freezing. We prove the
well-posedness, asymptotic stabilization, and thermodynamic
consistency of the model.
This is a joint work with Elisabetta Rocca and J\"urgen Sprekels.