Phase transitions in thermoelastic and thermoviscoelastic shells

Abstract

Applying the general non-linear theory of shells undergoing phase transitions, we derive the balance equations along the singular surface curve modelling the phase interface in the shell. From the integral forms of balance laws of linear momentum, angular momentum, and energy as well as the entropy inequality, we obtain the local static balance equations along the curvilinear phase interface. We discuss general forms of the constitutive equations for thermoelastic and thermoviscoelastic shells, as well as propose their simple cases for the linear isotropic shell behaviour. We also derive the thermodynamic condition allowing one to determine the interface position on the deformed shell midsurface. The theoretical model is illustrated by the example of thin circular cylindrical shell made of a two-phase elastic material subjected to tensile forces at the shell boundary. The solution reveals the existence of the hysteresis loop whose size depends upon values of several loading parameters.