Indentation of a non-equal biaxially stretched elastomer by an elliptic cone

By assuming the contact pressure follows an inverse hyperbolic cosine function and employing the surface Green's function method, we investigated the indentation of a non-equal biaxially stretched elastomer by an elliptic cone. We considered different rotation angles of the elliptic cone relative to the principal stretching directions of the elastomer and proposed a semi-analytical method to solve this problem. The rotation angle of the elliptic cone influences the relationship between the indentation force and the indentation depth. Additionally, we investigated the effects of the rotation angle of the elliptic cone and the pre-stretches of the elastomer on the rotation angle and eccentricity of the contact ellipse. By applying a pre-defined stress field to the elastomer, we performed finite element simulations of the present problem and found that the simulation results are in good agreement with the theoretical predictions. This work contributes to the application of indentation experiments to characterize the mechanical properties of pre-stretched soft materials, as well as to the design of contact or printing patterns.