Journal of elasticity and the physical science of solids

, Volume 66, Issue 2, pp 185–192

The Cauchy Relations in Linear Elasticity Theory

  • Friedrich W. Hehl
  • Yakov Itin

DOI: 10.1023/A:1021225230036

Cite this article as:
Hehl, F.W. & Itin, Y. Journal of Elasticity (2002) 66: 185. doi:10.1023/A:1021225230036


In linear elasticity, we decompose the elasticity tensor into two irreducible pieces with 15 and 6 independent components, respectively. The vanishing of the piece with 6 independent components corresponds to the Cauchy relations. Thus, for the first time, we recognize the group-theoretical underpinning of the Cauchy relations.

linear elasticityHooke's lawCauchy relations

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Friedrich W. Hehl
    • 1
  • Yakov Itin
    • 2
  1. 1.Institute for Theoretical PhysicsUniversity of CologneKölnGermany
  2. 2.Institute of MathematicsHebrew University of Jerusalem, JerusalemIsrael, and Jerusalem College of Engineering, Jerusalem 91035, Israel