Reduced elastic modulus ($E^{\ast }$)

The reduced elastic modulus combines the elastic compliance of two contacting isotropic bodies:Here $E_i$ is each body's Young's modulus and ${\nu }_i$ its Poisson's ratio. Both bodies deform under the same contact load, so their contributions to the indentation add. The factors involving Poisson's ratio account for the lateral constraint inherent in the local contact geometry.^[ref]

For identical materials, $E^{\ast }=E/[2(1-{\nu }^2)]$; against an effectively rigid probe, $E^{\ast }=E/(1-{\nu }^2)$ for the specimen. Thus even with a rigid probe, an indentation fit does not directly return Young's modulus. This matters when comparing Hertzian contact measurements with tensile testing, which imposes a different pattern of stress.