Nonlinear orthotropic elasticity: Only six invariants are independent

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It is often declared in the literature that the seven classical invariants used to characterize the strain energy of a compressible orthotropic elastic solid are independent. In this paper, we show that only six of the seven classical invariants are independent, and a syzygy exists between the classical invariants. Consequently, all other sets of seven invariants, proposed in the literature, that are uniquely related to the set of classical invariants, have only six independent invariants.

Original languageBritish English
Pages (from-to)237-241
Number of pages5
JournalJournal of Elasticity
Issue number2
StatePublished - Feb 2013


  • Elasticity
  • Independent
  • Invariants
  • Nonlinear
  • Orthotropic
  • Six


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