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

A hybrid extended finite element/level set method for modeling equilibrium shapes of nano-inhomogeneities