An Extended Hertz Model for Incompressible Mooney–Rivlin Half-Space Under Finite Spherical Indentation

Abstract

In this paper, an extended Hertz model is proposed to predict the mechanical responses of the incompressible Mooney–Rivlin half-space under finite spherical indentation. The contact behaviors are systematically investigated through the axisymmetric finite element (FE) model using various constitutive parameter ratios. Based on the numerical results, the radius of contact zone is first derived by adopting the exact function of the indenter shape. A reliable prediction of contact force, for the incompressible neo-Hookean model, is then obtained by substituting newly modified contact radius into the original Hertz model. From this base, a correction factor, which characterizes the effect of constitutive parameter ratio, is introduced to predict the contact force, and the contact pressure distribution of the original Hertz’ formula is also extended for the incompressible Mooney–Rivlin half-space under spherical indentation up to the indenter radius. The extended Hertz model related to constitutive parameters is validated effectively through FE simulations and experimental indentation results under finite spherical indentation. On the contrary, when the indentation depth exceeds 10% of the indenter radius, the original Hertz model is unable to predict the strong effect of constitutive parameter ratio on the contact behaviors for the incompressible Mooney–Rivlin half-space.