Non-standard and constitutive boundary conditions in nonlocal strain gradient elasticity Articles uri icon

publication date

  • March 2020

start page

  • 469

end page

  • 479


  • 3


  • 55

International Standard Serial Number (ISSN)

  • 0025-6455

Electronic International Standard Serial Number (EISSN)

  • 1572-9648


  • Zaera et al. (Int J Eng Sci 138:65–81, 2019) recently showed that the nonlocal strain gradient theory (NSGT) is not consistent when it is applied to finite solids, since all boundary conditions associated to the corresponding problems cannot be simultaneously satisfied. Given the large number of works using the NSGT being currently published in the field of generalized continuum mechanics, it is pertinent to evince the shortcomings of the application of this theory. Some authors solved the problem omitting the constitutive boundary conditions. In the current paper we show that, in this case, the equilibrium fields are not compatible with the constitutive equation of the material. Other authors solved it omitting the non-standard boundary conditions. Here we show that, in this case, the solution does not fulfil conservation of energy. In conclusion, the inconsistency of the NSGT is corroborated, and its application must be prevented in the analysis of the mechanical behaviour of nanostructures.


  • Materials science and engineering
  • Mechanical Engineering


  • conservation of energy; ill-posedness; nanobeams; non-standard boundary conditions; nonlocal strain gradient