Conditions for strong ellipticity of anisotropic elastic materials

Deren Han, H. H. Dai, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

73 Citations (Scopus)


In this paper, we derive necessary and sufficient conditions for the strong ellipticity condition of anisotropic elastic materials. We first observe that the strong ellipticity condition holds if and only if a second order tensor function is positive definite for any unit vectors. Then we further link this condition to the rank-one positive definiteness of three second-order tensors, three fourth-order tensors and a sixth-order tensor. In particular, we consider conditions of strong ellipticity of the rhombic classes, for which we need to check the copositivity of three second-order tensors and the positive definiteness of a sixth-order tensor. A direct method is presented to verify our conditions.
Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalJournal of Elasticity
Issue number1
Publication statusPublished - 1 Oct 2009


  • Anisotropic materials
  • Copositivity
  • Elasticity tensors
  • Rhombic systems
  • Strong ellipticity
  • Z-eigenvalues

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)


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