Acta Mechanica Sinica

, Volume 32, Issue 1, pp 83–100 | Cite as

A review on the application of modified continuum models in modeling and simulation of nanostructures

  • K. F. WangEmail author
  • B. L. Wang
  • T. Kitamura
Review Paper


Analysis of the mechanical behavior of nanostructures has been very challenging. Surface energy and nonlocal elasticity of materials have been incorporated into the traditional continuum analysis to create modified continuum mechanics models. This paper reviews recent advancements in the applications of such modified continuum models in nanostructures such as nanotubes, nanowires, nanobeams, graphenes, and nanoplates. A variety of models for these nanostructures under static and dynamic loadings are mentioned and reviewed. Applications of surface energy and nonlocal elasticity in analysis of piezoelectric nanomaterials are also mentioned. This paper provides a comprehensive introduction of the development of this area and inspires further applications of modified continuum models in modeling nanomaterials and nanostructures.

Graphic abstract


Surface elasticity Nonlocal continuum Nanotubes  Nanobeams Nanoplates Modeling and simulations 



The project was supported by the National Natural Science Foundation of China (Grant 11372086) and the Natural Science Foundation of Guangdong Province of China (Grant 2014A030313696).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Graduate School at ShenzhenHarbin Institute of TechnologyHarbinChina
  2. 2.Department of Mechanical EngineeringKyoto UniversityKyotoJapan

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