An analysis on stress field distribution of a deformable rubber specimen due to indentation

Knowledge of adherence phenomena in tire/road interaction is a key factor in the automotive field for safety and performance studies. In particular, many developments are focused on innovative tire structures and compounds, able to minimize braking distances, to preserve vehicle stability in panic situations and to guarantee optimal road holding on wet/icy surfaces. During road tire contact, two friction mechanisms prevail i.e. the adhesive and hysterical contribution. The complex tire/road interaction, as concerns macro roughness scale, is usually studied considering a rigid body (asphalt) which indents with a deformable body (rubber). The friction force deforming hysteresis component is a function of the time stress-field variation in the deformable body, due to indentation. The main aim of this study is to find out a formulation of the stress field in the rubber overcoming the limits of the one taken into account in the Gr.e.t.a. Model (Grip Estimation for Tire Analysis), based on the Kuznetsov–Gorokhovsky formulation. This approach shows evident limits being a bi-dimensional theory applied to a tri-dimensional domain. In this paper, an analysis on the stress field distribution of a deformable rubber parallelepiped specimen due to indentation has been conducted using the Hamilton formulation for stresses calculation. This theory refers to a deformable infinite half-space and it has been applied to a finite domain. To find out the minimum domain dimensions a finite element model has been developed, carrying out simulation under analogous working conditions, in no-sliding condition. The results show a good correlation between the numerical and analytical model in an opportunely dimensioned finite domain for the analyzed working condition.