Easy-to-compute tensors with symmetric inverse approximating hencky finite strain and its rate

Zdeněk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

It is shown that there exist approximations of the Hencky (logarithmic) finite strain tensor of various degrees of accuracy, having the following characteristics: (1) The tensors are close enough to the Hencky strain tensor for most practical purposes and coincide with it up to the quadratic term of the Taylor series expansion; (2) are easy t compute (the spectral representation being unnecessary); and (3) exhibit tensioncompression symmetry (i.e., the strain tensor of the inverse transformation is minus the original strain tensor). Furthermore, an additive decomposition of the proposed strain tensor into volumetric and deviatoric (isochoric) parts is given. The deviatoric part depends on the volume change, hut this dependence is negligible for materials that are incapable of large volume changes. A general relationship between the rate of the approximate Hencky strain tensor and the deformation rate tensor can be easily established.

Original languageEnglish (US)
Pages (from-to)131-136
Number of pages6
JournalJournal of Engineering Materials and Technology, Transactions of the ASME
Volume120
Issue number2
DOIs
StatePublished - Apr 1998

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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