Stress Tensor and Gradient of Hydrostatic Pressure in the Half-Space Beneath Axisymmetric Bodies in Normal and Tangential Contact

The stress state in the volume of contacting bodies may essentially influence the material behavior. For evaluating various modes of inelastic behavior and/or failure, such as plastic deformation, crack initiation, and propagation or fatigue, the complete stress tensor beneath the contact interface may be of importance. For many geotechnical and biomechanical applications, the hydrostatic pressure gradient beneath the contact is of interest as well. However, most theories for normal and tangential contact provide only few stress components in the contact surface. In the present paper, we show that the full stress state in the half-space can be easily found for axisymmetric bodies. We provide expressions in form of one-dimensional integrals for all components of the stress tensor and the hydrostatic pressure gradient inside the half-space. In terms of numerical complexity, the proposed method can be advantageous to other elaborate methods.