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On planar biaxial tests for anisotropic nonlinearly elastic solids. A continuum mechanical framework

Department of Solid Mechanics, School of Engineering Sciences, Royal Institute of Technology (KTH), Osquars Backe 1, SE-100 44 Stockholm, Sweden, Institute for Biomechanics, Center for Biomedical Engineering, Graz University of Technology, Kronesgasse 5-I, A-8010 Graz, Austria

Ray W. Ogden

Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK

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.

Key Words: biaxial testing • anisotropic material • elastic material • soft tissue mechanics • constitutive modeling • finite elasticity

This version was published on July 1, 2009

Mathematics and Mechanics of Solids, Vol. 14, No. 5, 474-489 (2009)
DOI: 10.1177/1081286507084411


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