Identifying hyperelastic and isotropic materials by examining the variation of principal direction of left Cauchy–Green deformation tensor in uniaxial loading

• Identified drawbacks in existing methods to find material symmetry.
• Existing mechanical test to identify material symmetry assume the body is homogeneous.
• Formulated new hypothesis to identify isotropic materials from uniaxial tests.
• New hypothesis identifies isotropic materials in inhomogeneous bodies as well.

Many bodies of biological and engineering interest have a fibrous and layered structure. Hence, it is believed that these bodies are inhomogeneous and made up of anisotropic material. Classical mechanical experiments used to find the required material symmetry in the constitutive relation cannot distinguish inhomogeneous bodies made of isotropic material and homogeneous bodies made of anisotropic material. Therefore, it is of interest to find an alternative hypothesis so that inhomogeneity and anisotropy can be determined independent of the other. This study finds that the principal (or eigen) direction of the left Cauchy–Green deformation tensor, BB does not vary with the magnitude of the applied uniaxial load at a given location whenever the body – homogeneous or inhomogeneous – is made of isotropic and hyperelastic material and the deformations are measured from a stress free reference configuration. In general, the principal direction of the left Cauchy–Green deformation tensor varies with the magnitude of the uniaxial load when the body is made up of anisotropic material. Thus, it is concluded that if the variation in the principal direction of BB with the magnitude of the applied uniaxial load is experimentally investigated then one could ascertain whether the body is made up of isotropic or anisotropic material.