  In this paper, we formulate a continuum theory of solidification within the
context of finite-strain coupled thermoelasticity. We aim to fill a gap in the
existing literature, as the existing studies on solidification typically
decouple the thermal problem (the classical Stefan's problem) from the
elasticity problem, and often limit themselves to linear elasticity with small
strains. Treating solidification as an accretion problem, with the growth
velocity correlated with the jump in the heat flux across the boundary, it
presents an initial boundary-value problem (IBVP) over a domain whose boundary
location is a priori unknown. This IBVP is solved numerically for the specific
example of radially inward solidification in a spherical container. Several
parametric studies are conducted to compare the numerical results with the
rigid cases in the literature and gain insights into the role of elastic
deformations in solidification.
