An extended Maugis-Dugdale model for viscoelastic spherical adhesive contact

This paper presents a full viscoelastic extension of the MD (Maugis-Dugdale) model by conducting the convolution of Maugis' linear elastic crack shape and an impulse response of a three-element viscoelastic solid. The formula for the effective surface energy is provided.Greenwood's effective surface energy is ours at m=1. Maugis' formulae for the applied load and the contact displacement are rewritten in the form of the effective surface energy. When m=1, the rewritten Maugis' formulae will be reduced to the viscoelastic JKR (Johnson-Kendall-Roberts) model. Substituting our effective surface energy into the rewritten Maugis' formulae, the unloading process of the viscoelastic spherical adhesive contact can be described. In comparison with Ciavarella's work, it is found that Ciavarella's viscoelastic extension is an approximation of ours.