Determining Prestrains in an Elastomer Through Elliptical Indentation

Residual stresses or prestrains could strongly affect the properties and functionalities of soft materials and tissues. However, non-destructive measurements of residual stresses or prestrains in materials are generally challenging. Previous studies have shown that residual stresses or prestrains can affect indentation tests of different materials, including metals, glassy polymers, soft elastomers, and gels. Nevertheless, an indentation method for determining the state of residual stresses or prestrains of large magnitude in an elastomer is not yet available. In this article, we propose to use elliptical indentation to measure large prestretches in a Neo-Hookean elastomer. We have analytically derived the relationship between the indentation force and indentation depth for both a flat-ended elliptical indenter and an ellipsoidal indenter. We have further shown that such a relationship greatly depends on the rotational angle of the indenter with respect to the direction of principle stretches in the elastomer. Based on the derived analytical results, we construct two diagrams for the flat-ended elliptical indenter and ellipsoidal indenter, respectively, which can be directly used to determine quantitatively large prestrains in an elastomer.