Dynamic Contact Stress Determination Method for the Normal Collision Between Rigid Sphere and Elastic Half-space Interface

The Hertz theory's reliance on static equilibrium assumptions limits its applicability to dynamic scenarios. This article addresses the gap regarding the dynamic normal stress at the contact interface between rigid sphere and elastic half-space. Based on the physical characteristics of dynamic contact and mass point dynamics theory, dynamic equations of the interface mass point is established. By decoupling these equations based on the lateral and tangential motion of the mass point, we derive a unified normal motion equation that describes the relative relationship between the normal strain of each mass point and the interface center point. The equation demonstrates that the lateral and tangential strains prior to collision do not directly affect the sphere motion in the normal direction, while the incremental lateral and tangential strains after post-collision significantly do. The lateral stress increment, tangential stress increment, and the distribution law of normal stress for each mass point at the interface are obtained. The results demonstrate that the relative relationship between the maximum deformation depth in the non-contact area and that in the contact area, as well as the relative relationship between the isotropic stress of the contact area and the normal stress at the collision center, are consistent with the results determined by Hertz theory, but the obtained normal stress value is significantly greater than that determined by Hertz theory and the detailed discrepancies are compared. The findings have implications for understanding and predicting contact interface failure in engineering applications, particularly under dynamic loading conditions.