Contact Model for Incompressible Neo-Hookean Materials under Finite Spherical Indentation

In this paper, a contact model is proposed to predict the contact response of an incompressible neo-Hookean half-space under finite spherical indentations. The axisymmetric finite element (FE) model is created to simulate the contact behaviors. Inspired by the numerical results, the radius of the contact circle is derived. The contact force is then obtained by modifying the radius of the contact circle of the Hertz model. The format of the distribution of the contact pressure is also developed according to the Hertz model. A parameter, determined by fitting the numerical results, is introduced to characterize the effect of the indentation depth on the shape of the distribution function of the contact pressure. The newly proposed contact model is numerically validated to predict well the contact behaviors, including the contact force, the radius of the contact circle, and the distribution of the contact pressure, for the incompressible neo-Hookean half-space under spherical indentation up to the indenter radius. However, the Hertz model is verified to offer acceptable predictions of the contact behaviors for the incompressible neo-Hookean materials within the indentation depth of 0.1 times of the indenter radius.