A new method is developed in the present study to determine the elastoplastic regime of a spherical asperity in terms of the interference of two contact surfaces. This method provides an efficient way to solve the problem of discontinuities often present in the reported solutions for the contact load and area or the gradients of these parameters obtained at either the inception or the end of the elastoplastic regime. The well-established solutions for the elastic regime and experimental data of metal materials using indentation tests are provided as the references to determine the errors of these contact parameters due to the use of the finite-element method. These numerical errors provide the basis to adjust the contact area and contact load of a rigid sphere in contact with a flat such that the dimensionless mean contact pressure $Pave∕Y$ ($Y$: the yielding strength) and the dimensionless contact load $Fpc∕Fec$ ($Fec$, $Fpc$: the contact loads corresponding to the inceptions of the elastoplastic and fully plastic regimes, respectively) reaches the criteria arising at the inception of the fully plastic regime, which are available from the reports of the indentation tests for metal materials. These two criteria are however not suitable for the present case of a rigid flat in contact with a deformable sphere. In the case of a rigid flat in contact with a deformable sphere, the proportions in the adjustments of these contact parameters are given individually the same as those arising in the indentation case. The elastoplastic regime for each of these two contact mechanisms can thus be determined independently. By assuming that the proportion of adjustment in the elastoplastic regime is a linear function, the discontinuities appearing in these contact parameters are absent from the two ends of the elastoplastic regime in the present study. These results are presented and compared with the published results.

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