On mindlins isotropic strain gradient elasticity: Green tensors, regularization, and operator-split

Markus Lazar, Giacomo Po

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The theory of Mindlins isotropic strain gradient elasticity of form II is reviewed. Three-dimensional and two-dimensional Green tensors and their first and second derivatives are derived for an unbounded medium. Using an operator-split in Mindlins strain gradient elasticity, three-dimensional and two-dimensional regularization function tensors are computed, which are the three-dimensional and two-dimensional Green tensors of a tensorial Helmholtz equation. In addition, a length scale tensor is introduced, which is responsible for the characteristic material lengths of strain gradient elasticity. Moreover, based on the Green tensors of Mindlins strain gradient elasticity, point, line and double forces are studied.

Original languageEnglish (US)
Article number1840008
JournalJournal of Micromechanics and Molecular Physics
Volume3
Issue number3-4
DOIs
StatePublished - Sep 2018
Externally publishedYes

Keywords

  • Gradient elasticity
  • Green function
  • Modified Green function
  • Operator-split
  • Regularization

ASJC Scopus subject areas

  • Ceramics and Composites
  • Polymers and Plastics
  • Atomic and Molecular Physics, and Optics
  • Mechanics of Materials

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