Length scale dependence in elastomers - Comparison of indentation experiments with numerical simulations

Probing depth dependent deformation at nano- and micrometer length scales has been observed in indentation experiments of polymers. Unlike in metals, where size effects are observed in plastic deformation and are attributed to geometrically necessary dislocations, the origin of size dependence in polymers is not well understood. As classical continuum theories are unable to describe such phenomena, higher order gradient theories have been developed to capture such size dependent deformation behavior. The present study adopts the penalty finite element approach for a couple stress elasticity theory under axisymmetric conditions to numerically simulate and analyze the probing depth dependent deformation. Polydimethylsiloxane (PDMS) and natural rubber have been used as model materials to analyze the depth dependent deformation at different probing depths. Simulations were performed on PDMS using spherical indenter tips of different radii to show the influence of strain/rotation gradients on elastic modulus. To capture the experimentally observed increase in hardness with decreasing probing depth, simulations applying a conical indenter tip were performed and compared with experimental data.