The non-singular Green tensor of Mindlin's anisotropic gradient elasticity with separable weak non-locality

Markus Lazar, Giacomo Po

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

In this paper, we derive the Green tensor of anisotropic gradient elasticity with separable weak non-locality, a special version of Mindlin's form II anisotropic gradient elasticity theory with up to six independent length scale parameters. The framework models materials where anisotropy is twofold, namely the bulk material anisotropy and a weak non-local anisotropy relevant at the nano-scale. In contrast with classical anisotropic elasticity, it is found that both the Green tensor and its gradient are non-singular at the origin, and that they rapidly converge to their classical counterparts away from the origin. Therefore, the Green tensor of Mindlin's anisotropic gradient elasticity with separable weak non-locality can be used as a physically-based regularization of the classical Green tensor for materials with strong anisotropy.

Original languageEnglish (US)
Pages (from-to)1538-1543
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume379
Issue number24-25
DOIs
StatePublished - Jul 31 2015
Externally publishedYes

Keywords

  • Anisotropy Green tensor
  • Gradient elasticity
  • Nano-elasticity
  • Non-locality
  • Regularization

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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