Extracting the isotropic uniaxial stress-strain relationship of hyperelastic soft materials based on new nonlinear indentation strain and stress measure

Instrumented indentation technique has been increasingly utilized to measure the mechanical properties of soft polymers and biological tissues. However, the indentation behaviors of these materials has not been well understood, especially the parameter identification of their hyperelastic material properties. In this paper, we developed a spherical indentation data analysis method to directly extract the isotropic uniaxial stress-strain relationship of hyperelastic soft materials from the measured spherical indentation load-displacement curves. The proposed method mainly included new measure of indentation stress and strain, which was built based on the Hertz load-displacement relationship and further revised by considering the non-Hertzian effects of neo-Hookean hyperelastic contact problems. Numerical and actual indentation experiments showed the proposed definition of indentation strain can properly evaluate the amount of nonlinear strain for neo-Hookean, Yeoh and Arruda-Boyce hyperelastic materials. Meanwhile, the proposed spherical indentation data analysis method was applicable only in certain deformation range for Yeoh and Arruda-Boyce hyperelastic materials, because their nonlinear material parameters might cause very complicated contact pressure distributions. Building a universal data processing technique for characterizing the hyperelastic mechanical properties of soft materials through indentation experiments still needed further investigations.