  While statistical mechanics provides a comprehensive framework for the
understanding of equilibrium phase behavior, predicting the kinetics of phase
transformations remains a challenge. Classical nucleation theory (CNT) provides
a thermodynamic framework to relate the nucleation rate to thermodynamic
quantities such as pressure difference and interfacial tension through the
nucleation work necessary to spawn critical nuclei. However, it remains unclear
whether such an approach can be extended to the crystallization of driven melts
that are subjected to mechanical stresses and flows. Here, we demonstrate
numerically for hard spheres that the impact of simple shear on the
crystallization rate can be rationalized within the CNT framework by an
additional elastic work proportional to the droplet volume. We extract the
local stress and strain inside solid droplets, which yield size-dependent
values for the shear modulus that are about half of the bulk value. Finally, we
show that for a complete description one also has to take into account the
change of interfacial work between the strained droplet and the sheared liquid.
From scaling reasons, we expect this extra contribution to dominate the work
formation of small nuclei but become negligible compared to the elastic work
for droplets composed of a few hundreds particles.
