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

TL;DR

This paper introduces a hybrid finite element/level set numerical method to accurately model equilibrium shapes of nanoscale inhomogeneities considering interfacial energy effects, improving efficiency and accuracy over existing methods.

Contribution

It develops a novel hybrid smoothed extended finite element/level set approach that handles interface geometry independently and incorporates surface elasticity effects using Wachspress interpolants.

Findings

The method accurately predicts equilibrium shapes consistent with theoretical and experimental results.

It demonstrates superior computational efficiency compared to existing advanced methods.

Numerical results validate the effectiveness of the hybrid approach for nanoscale microstructure modeling.

Abstract

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.