Can hyperelastic material parameters be uniquely determined from indentation experiments?

Abstract

Indentation experiments have been widely adopted to evaluate the hyperelastic material properties of soft polymers and biological tissues. However, due to the combination of constitutive, geometric and contact nonlinearities, the hyperelastic indentation problem has not been solved analytically. The hyperelastic parameters extracted from the indentation load–displacement curve are poorly defined. Even the uniqueness of these parameters remains unknown. This work determines the uniqueness of hyperelastic material parameters by conducting dimensional analysis based on different combinations of hyperelastic models (which include constitutive nonlinearity) and the shapes of indenters (which reflect geometric and contact nonlinearities). It is proved that the unique determination of hyperelastic material parameters depends on a simple criterion: whether the dimensionless hyperelastic parameters are coupled with indentation displacement or not. Furthermore, for the indentation problems in which unique hyperelastic material parameters cannot be guaranteed, a unique measure is constructed and validated by experiments on biomedical polymers.