Author(s)

R. Guilbault

Abstract

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 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 FEM 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  of 0,15, the maximum error was -11,30%, which was reduced to +0,60% with the ψ factor. Keywords: quarter-space, quarter-plane, free surface, contact model, Boussinesq–Cerruti solution, normal load. 1 Introduction and literature survey The Hertz theory can be applied to some non-Hertzian contact problems, and lead to acceptable results even when basic hypotheses are not fully respected. Such applications remain but approximated treatments, since the Hertz theory does not include the influence of free surfaces. In reality, including the influence of free surfaces requires numerical methods, the best-known being the finite element method (FEM). However, the computation time of FEM contact models can still have detrimental consequences. Fortunately, other accurate numerical

Keywords

quarter-space, quarter-plane, free surface, contact model, Boussinesq–Cerruti solution, normal load