Nonlinear elastic load–displacement relation for spherical indentation on rubberlike materials

Because of the lack of universal contact models for nonlinear strain problems, indentation analysis on rubberlike materials is confined to small deformation in which Hertz's solution is applied. Recognizing that deep indentation may provide more material information, in this paper we propose a nonlinear elastic model for large spherical indentation of rubberlike materials based on the higher-order approximation of spherical function and Sneddon's solution. The effect of limiting network stretch is studied on the initial elastic modulus for lightly cross-linked rubbers. With the comparisons of the finite-element simulation and the experimental result, the proposed model is verified to predict the large indentation of rubberlike materials over the indentation depth of 0.8 times the indenter radius.