A Fast Correction for Elastic Quarter-Space Applied to 3D Modeling of Edge Contact Problems

Applying the Hertz theory to some non-Hertzian contact problems can produce acceptable results. Nevertheless, including the influence of free surfaces requires numerical methods, many of which are based on the Boussinesq–Cerruti solution. This paper presents a new approach, which is better capable of releasing quarter-space free surfaces from shear and normal internal stresses without engendering any increase in calculation times. The mirrored pressure for shear correction is multiplied by a correction factor $(ψ)$⁠, which accounts for the normal load. The expression $ψ$ is derived from the Hetényi correction process, and the resulting displacements show an enhanced correspondence with validation finite element method models; with an imposed fluctuating pressure, the maximum edge displacement error was −21.90% for a shear load correction (Poisson coefficient $ν=0.3$⁠), and introducing the $ψ$ factor reduced the deviation to −9.55%, while for $ν$ of 0.15, the maximum error was −11.30%, which was reduced to $+0.60%$ with the $ψ$ factor. This study introduces the factor $ψ$ in a 3D elastic contact algorithm. The resulting calculation scheme is then able to simulate any point or line contact problems. Compared with coincident ends and sharp edge contact validation values, the model shows high conformity levels.