Investigation of spherical contact with different degrees of geometric conformity for elastic and elasto-plastic materials.

This work presents a parametric numerical procedure for the analysis of contact between a sphere and a spherical-cavity seat over different degrees of geometric conformity. The model is developed in ANSYS Mechanical APDL with MATLAB support and is based on an axisymmetric formulation, allowing the automatic generation of geometry, mesh, contact conditions and post-processing routines from a limited set of input parameters: the radii of the bodies, the imposed indentation depth, the macro dimensions of the involved bodies and the material properties.

The procedure provides a flexible and repeatable framework for studying contact configurations that range from non-conformal to highly conformal cases. The numerical model is first assessed against Hertz theory in the non-conformal elastic regime, where pressure distribution, contact radius and force-indentation response can be compared with closed-form solutions. Conformal configurations are then examined through comparison with the Winkler-based formulation. In this case, the validation focuses on the normal relative displacement field, the pressure field obtained through the local proportionality between pressure and displacement, and the resulting global force response obtained by integration over the contact region. This allows the verification of both the local contact behaviour and the overall stiffness predicted by the numerical model. The onset of plasticity is also evaluated through Hertzian estimates of initial yielding, which are used as an analytical reference for interpreting the numerical results. The analysis considers the main quantities characterizing the contact problem, including pressure profiles, force-indentation curves, Von Mises equivalent stress and equivalent plastic strain.

 Attention is given to the consistency of the automated workflow and to the influence of the adopted discretization on local and global contact quantities. The procedure provides a structured numerical tool for investigating both conformal and non-conformal spherical contacts under elastic and elasto-plastic material behaviour in a repeatable manner.