The general 3D Hertzian contact problem for anisotropic materials

Abstract

This paper presents a general method for solving the 3D frictionless contact problem between generally anisotropic materials with any second order surface geometry. The method uses the Stroh formalism to find the Green's Functions (GF) of the materials with an efficient numerical integration process. The GFs are then expanded in Fourier series in order to solve the Hertzian contact problem between the two bodies as a perturbation to the first order, 2equivante isotropic2, solution to the problem. The latter permits to define an 2equivalent indentation modulus of the contact" which is a single parameter computed from the first terms of the Fourier expansion of the two GFs (ie the average values) and permits to use the standard Hertzian solution: this gives a good approximation to the contact area (at most elliptical in any case) which is approximated as a circle for axi-symmetrical geometry, and for the approach of remote points in the two bodies. The "equivalent indentation modulus", which depends on materials and orientation, is computed for a set of composite materials of practical interest