The non-singular Green tensor of gradient anisotropic elasticity of Helmholtz type

Markus Lazar, Giacomo Po

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

In this paper, we derive the three-dimensional Green tensor of the theory of gradient anisotropic elasticity of Helmholtz type, a particular version of Mindlin's theory of gradient elasticity with only one characteristic parameter. In contrast with classical anisotropic elasticity, it is found that in gradient anisotropic elasticity of Helmholtz type both the Green tensor and its gradient are non-singular at the origin. On the other hand, the Green tensor rapidly converges to its classical counterpart a few characteristic lengths away from the origin. Therefore, the Green tensor of gradient anisotropic elasticity of Helmholtz type can be used as a physically-based regularization of the classical anisotropic Green tensor. Using the non-singular Green tensor, the Kelvin problem is studied in the framework of gradient anisotropic elasticity.

Original languageEnglish (US)
Pages (from-to)152-162
Number of pages11
JournalEuropean Journal of Mechanics, A/Solids
Volume50
DOIs
StatePublished - 2015
Externally publishedYes

Keywords

  • Anisotropy
  • Gradient elasticity
  • Green tensor

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

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