Hyperelastic characterization via deep indentation

Abstract

Hyperelastic material characterization is crucial for understanding the behavior of soft materials—such as tissues, rubbers, hydrogels, and polymers—under quasi-static loading before failure. Traditional methods typically rely on uniaxial tensile tests, which require the cumbersome preparation of dumbbell-shaped samples for clamping in a uniaxial testing machine. In contrast, indentation-based methods, which can be conducted in-situ without sample preparation, have been underexplored. To characterize the hyperelastic behavior of soft materials, deep indentation is required, where the material response extends beyond linear elasticity. In this study, we perform finite element analysis to link the force (F) vs. indentation depth (D) curve with the hyperelastic behavior of a soft incompressible material, using a one-term Ogden model for simplicity. We identify three indentation regimes based on the ratio between indentation depth and the radius (R) of the spherical-tipped cylindrical indenter: (1) the Hertzian regime (D<0.1 R) with F=ER^0.5 D^1.5 16/9, (2) the parabolic regime (D>10 R) with F=ED^2 β, where the indenter radius becomes irrelevant, and (3) an intermediate regime (0.1 R>3, friction has a negligible effect. We validate this approach through uniaxial and deep indentation experiments on four representative materials, showing good agreement between the two methods and confirming the effectiveness of deep indentation for extracting hyperelastic parameters via in-situ testing.