Fig. 2.

FEA results for the Mooney-Rivlin and Ogden hyperelastic materials. a Theoretical equation (2) and FEA-derived, Mooney-Rivlin contact radii as functions of the indentation. Both contact radius and indentation are normalized by the radius of the sphere. The least squares fit of the large displacement FEA data was performed using Eq. (13); the unit of length is nm. Note that since Eq. (13) has three fitting parameters, this solution is not unique. Data for the Ogden case is virtually identical. b Comparison of Eq. (2) and FEA-derived, Mooney-Rivlin contact radii at small displacement. For this case, differences between Mooney-Rivlin, Ogden, and Hertz models were negligible. c Indentation stress–strain curves using the definitions in Eqs. (3). FEA and the theoretical Ogden model from Table 2 both indicate significant nonlinearity. d Vertical strain field in the Ogden material at maximum indentation (δ = R). The maximum compressive strain of ~46% occurs at the point of initial contact, but the average value is in line with the definition ε^* = 0.2a/R