Revisiting the Maugis–Dugdale Adhesion Model of Elastic Periodic Wavy Surfaces

Abstract

The plane strain adhesive contact between a periodic wavy surface and a flat surface has been revisited based on the classical Maugis–Dugdale model. Closedform analytical solutions derived by Hui et al. [1], which were limited to the case that the interaction zone cannot saturate at a period, have been extended to two additional cases with adhesion force acting throughout the whole period. Based on these results, a complete transition between the Westergaard and the Johnson, Kendall, and Roberts (JKR)type contact models is captured through a dimensionless transition parameter, which is consistent with that for a single cylindrical contact. Depending on two dimensionless parameters, different transition processes between partial and full contact during loading/unloading stages are characterized by one or more jump instabilities. Rougher surfaces are found to enhance adhesion both by increasing the magnitude of the pulloff force and by inducing more energy loss due to adhesion hysteresis.