  Interfacial energy plays an important role in equilibrium morphologies of
nanosized microstructures of solid materials due to the high
interface-to-volume ratio, and can no longer be neglected as it does in
conventional mechanics analysis. The present work develops an effective
numerical approach by means of a hybrid smoothed extended finite element/level
set method to model nanoscale inhomogeneities with interfacial energy effect,
in which the finite element mesh can be completely independent of the interface
geometry. The Gurtin-Murdoch surface elasticity model is used to account for
the interface stress effect and the Wachspress interpolants are used for the
first time to construct the shape functions in the smoothed extended finite
element method. Selected numerical results are presented to study the accuracy
and efficiency of the proposed method as well as the equilibrium shapes of
misfit particles in elastic solids. The presented results compare very well
with those obtained from theoretical solutions and experimental observations,
and the computational efficiency of the method is shown to be superior to that
of its most advanced competitor.
