On planar biaxial tests for anisotropic nonlinearly elastic solids

Gerhard Holzapfel, Raymond W. Ogden

Research output: Contribution to journalArticlepeer-review

160 Citations (Scopus)


The mechanical testing of anisotropic nonlinearly elastic solids is a topic of considerable and increasing interest. The results of such testing are important, in particular, for the characterization of the material properties and the development of constitutive laws that can be used for predictive purposes. However, the literature on this topic in the context of soft tissue biomechanics, in particular, includes some papers that are misleading since they contain errors and false statements. Claims that planar biaxial testing can fully characterize the three-dimensional anisotropic elastic properties of soft tissues are incorrect. There is therefore a need to clarify the extent to which biaxial testing can be used for determining the elastic properties of these materials. In this paper this is explained on the basis of the equations of finite deformation transversely isotropic elasticity, and general planar anisotropic elasticity. It is shown that it is theoretically impossible to fully characterize the properties of anisotropic elastic materials using such tests unless some assumption is made that enables a suitable subclass of models to be preselected. Moreover, it is shown that certain assumptions underlying the analysis of planar biaxial tests are inconsistent with the classical linear theory of orthotropic elasticity. Possible sets of independent tests required for full material characterization are then enumerated.
Original languageEnglish
Pages (from-to)474-489
Number of pages16
JournalMathematics and Mechanics of Solids
Issue number5
Early online date11 Mar 2008
Publication statusPublished - 2009


  • biaxial testing
  • anisotropic material
  • elastic material
  • soft tissue mechanics
  • constitutive modeling


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