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

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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. When designing nanodevices and to understand the behavior of materials at the nano-scale, this interfacial energy must therefore be taken into account. 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.

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Acknowledgments

XZ and JQ acknowledge the partial support by NSF through CMMI-1200075. SPAB acknowledges partial support from the European Research Council Starting Independent Research Grant (ERC Stg No. 279578) and EPSRC’s grants EP/G042705/1 and EP/I006761/1.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Northwestern University, Evanston, IL, 60208, USA

    Xujun Zhao & Jianmin Qu

  2. Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL, 60208, USA

    Jianmin Qu

  3. Cardiff School of Engineering, Institute of Mechanics and Advanced Materials Theoretical, Applied and Computational Mechanics, Cardiff University, The Parade, Cardiff, Wales, CF24 3AA, UK

    Stéphane P. A. Bordas

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  1. Xujun Zhao
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  2. Stéphane P. A. Bordas
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  3. Jianmin Qu
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Correspondence to Stéphane P. A. Bordas or Jianmin Qu.

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Stéphane P. A. Bordas’s ORCID ID is 0000-0001-7622-2193.

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Zhao, X., Bordas, S.P.A. & Qu, J. A hybrid smoothed extended finite element/level set method for modeling equilibrium shapes of nano-inhomogeneities. Comput Mech 52, 1417–1428 (2013). https://doi.org/10.1007/s00466-013-0884-1

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