Hyperelastic characterization via deep indentation

Area of Science:

• Materials Science
• Solid Mechanics
• Biomechanics

Background:

• Hyperelastic material characterization is vital for understanding soft materials like tissues and polymers.
• Traditional uniaxial tensile tests require complex sample preparation and are not suitable for in situ analysis.
• Indentation-based methods offer a non-destructive, in situ alternative but require deep indentation for hyperelastic characterization.

Purpose of the Study:

• To establish a link between force-depth indentation curves and hyperelastic behavior using finite element analysis.
• To identify and analyze different indentation regimes (Hertzian, parabolic, intermediate) for soft incompressible materials.
• To investigate the influence of material properties (Ogden strain-stiffening coefficient) and friction on indentation response.

Main Methods:

• Finite element analysis (FEA) was employed to model the indentation of soft incompressible materials.
• A one-term Ogden model was used to represent the hyperelastic material behavior.
• Force (F) vs. indentation depth (D) curves were analyzed across different indentation regimes (D/R ratios).

Main Results:

• Three distinct indentation regimes were identified: Hertzian (D ≪ R), parabolic (D ≫ R), and an intermediate regime.
• The Ogden strain-stiffening coefficient (α) was found to increase the parabolic indentation coefficient (β), enabling α estimation from β.
• Coulomb friction was observed to increase β, potentially masking strain-stiffening effects for small α, but becoming negligible for α > 3.
• Experimental validation on various soft materials (Ecoflex, Mold Star, porcine skin) showed good agreement with the predicted power-law regimes.

Conclusions:

• Deep indentation provides a universal parabolic force-depth scaling, offering a reliable method for hyperelastic property extraction.
• Indentation-based characterization is a practical and effective alternative to conventional tensile testing for in situ analysis of soft materials.
• The study demonstrates the feasibility of extrapolating hyperelastic properties (α and E) from indentation data with high accuracy (within 20% deviation).