Considerations on incompressibility in linear elasticity

S. Federico*, A. Grillo, G. Wittum

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The classical way to treat incompressible linear elastic materials is to use the inverse constitutive relationship (strain as a function of the stress), based on the compliance tensor, in place of the direct constitutive equation (stress as a function of strain), based on the elasticity (stiffness) tensor. This is because the elasticity tensor is affected by a diverging bulk modulus, required in order to allow the material to sustain any hydrostatic load, and is therefore not defined. In this work we show that there is a part of the elasticity tensor that can be "saved" also for incompressible materials, by "filtering" the components that deal with hydrostatic loads. The procedure is based on the treatment of incompressibility by means of the constraint of isochoric motion, i.e. of conservation of volume, and fourth-order tensor algebra.

Original languageEnglish (US)
Pages (from-to)81-87
Number of pages7
JournalNuovo Cimento della Societa Italiana di Fisica C
Issue number1
StatePublished - 2009
Externally publishedYes

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Physics and Astronomy (miscellaneous)


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