A double-Westergaard model for adhesive contact of a wavy surface

This paper extends the double-Hertz model of Greenwood and Johnson (1998) to the plane strain problem of adhesive contact between a wavy surface and a flat surface, named as the double-Westergaard model. The adhesive force within the cohesive zone near contact edge is described by the difference between two Westergaard pressure distribution functions with different contact widths. Closed-form analytical solutions are obtained for different equilibrium states during loading and unloading stages. The proposed model captures a transition between Westergaard and JKR contact models through a dimensionless transition parameter. Depending on two dimensionless parameters, transitions between partial and full contact during loading/unloading are characterized by one or more jump instabilities. Decreasing waviness size by decreasing both the amplitude and period with a fixed curvature is found to enhance adhesion both by increasing the magnitude of the pull-off force and by inducing more energy loss through adhesion hysteresis.