Stability and finite strain of homogenized structures soft in shear: Sandwich or fiber composites, and layered bodies

Zdeněk P. Bažant*, Alessandro Beghini

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

The stability theories energetically associated with different finite strain measures are equivalent if the tangential moduli are transformed as a function of the stress. However, for homogenized soft-in-shear composites, they can differ greatly if the material is in small-strain and constant elastic moduli measured in small-strain tests are used. Only one theory can then be correct. The preceding variational energy analysis showed that, for sandwich columns and elastomeric bearings, respectively, the correct theories are Engesser's and Haringx's, associated with Green's and Almansi's Lagrangian strain tensors, respectively. This analysis is reviewed, along with supporting experimental and numerical results, and is then extended to arbitrary multiaxially loaded homogenized soft-in-shear orthotropic composites. It is found that, to allow the use of constant shear modulus when the material is in small strain, the correct stability theory is associated with a general Doyle-Ericksen finite strain tensor of exponent m depending on the principal stress ratio. Further it is shown that the standard updated Lagrangian algorithm for finite element analysis, which is associated with Green's Lagrangian finite strain, can give grossly incorrect results for homogenized soft-in-shear structures and needs to be generalized for arbitrary finite strain measure to allow using constant shear modulus for critical loads at small strain.

Original languageEnglish (US)
Pages (from-to)1571-1593
Number of pages23
JournalInternational Journal of Solids and Structures
Volume43
Issue number6
DOIs
StatePublished - Mar 2006

Keywords

  • Buckling
  • Composites
  • Critical loads
  • Elastomeric bearings
  • Finite element analysis
  • Finite strain
  • Homogenization
  • Layered bodies
  • Numerical algorithm
  • Sandwich structures
  • Stability

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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