Conical indentation of incompressible rubber-like materials

Abstract

In the last decade, the indentation test has become a useful tool for probing mechanical properties of small material volumes. In this context, little has been done for rubber-like materials (elastomers), although there is pressing need to use instrumented indentation in biomechanics and tissue examination. The present work investigates the quasi-static normal instrumented indentation of incompressible rubber-like substrates by sharp rigid cones. A second-order elasticity analysis was performed in addition to finite element analysis and showed that the elastic modulus at infinitesimal strains correlates well with the indentation response that is the relation between the applied force and the resulting vertical displacement of the indentor’s tip. Three hyperelastic models were analyzed: the classic Mooney–Rivlin model, the simple Gent model and the one-term Ogden model. The effect of the angle of the cone was investigated, as well as the influence of surface friction. For blunt cones, the indentation response agrees remarkably well with the prediction of linear elasticity and confirms available experimental results of instrumented Vickers indentation.