Indentation of a stretched elastomer

Indentation has been intensively used to characterize mechanical properties of soft materials such as elastomers, gels, and soft biological tissues. In most indentation measurements, residual stress or stretch which can be commonly found in soft materials is ignored. In this article, we aim to quantitatively understand the effects of prestretches of an elastomer on its indentation measurement. Based on surface Green's function, we analytically derive the relationship between indentation force and indentation depth for a prestretched Neo-Hookean solid with a flat-ended cylindrical indenter as well as a spherical indenter. In addition, for a non-equal biaxially stretched elastomer, we obtain the equation determining the eccentricity of the elliptical contacting area between a spherical indenter and the elastomer. Our results clearly demonstrate that the effects of prestretches of an elastomer on its indentation measurement can be significant. To validate our analytical results, we further conduct correspondent finite element simulations of indentation of prestretched elastomers. The numerical results agree well with our analytical predictions.