Universal elastic anisotropy index

Shivakumar I. Ranganathan, Martin Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review


Practically all elastic single crystals are anisotropic, which calls for an appropriate universal measure to quantify the extent of anisotropy. A review of the existing anisotropy measures in the literature leads to a conclusion that they lack universality in the sense that they are nonunique and ignore contributions from the bulk part of the elastic stiffness (or compliance) tensor. Proceeding from extremal principles of elasticity, we introduce a new universal anisotropy index that overcomes the above limitations. Furthermore, we establish special relationships between the proposed anisotropy index and the existing anisotropy measures for special cases. A new elastic anisotropy diagram is constructed for over 100 different crystals (from cubic through triclinic), demonstrating that the proposed anisotropy measure is applicable to all types of elastic single crystals, and thus fills an important void in the existing literature.

Original languageEnglish (US)
Article number055504
JournalPhysical review letters
Issue number5
StatePublished - Aug 1 2008

ASJC Scopus subject areas

  • Physics and Astronomy(all)


Dive into the research topics of 'Universal elastic anisotropy index'. Together they form a unique fingerprint.

Cite this