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Recently, a simple and elegant "dimple" model was introduced by McMeeking etal. (Adv Eng Mat 12(5), 389-397, 2010) to show a mechanism for a bistableadhesive system involving a surface with a shallow depression. The systemshows, at least for intermediate levels of stickiness, that external pressurecan switch the system into a "strong adhesive" regime of full contact, or intoweak adhesion and complete pull-off, similarly to the contact of surfaces witha single scale of periodical waviness. We add to this model the effect ofroughness, in the simple form of axisymmetric single scale of waviness,permitting a very detailed study, and we show that this induces a resistance tojumping into full contact on one hand (limiting the "strong adhesion" regime),and an enhancement of pull-off and of hysteresis starting from the partialcontact state on the other (enhancing the "weak adhesion" regime). We show thesystem depends only on two dimensionless parameters, depending on the ratio ofwork of adhesion to the energy to flatten the dimple or waviness, respectively.The system becomes pressure-sensitive also in the intermediate states, as it isobserved in real adhesive rough systems. The model obviously is specular to theGuduru model of rough spheres (Guduru, JMPS, 55, 473--488, 2007), with which itshares the limitations of the analysis assuming a connected contact (crack)area, and serves also the purpose of showing the effect of a depression into anotherwise periodic rough contact, towards the understanding of adhesion withmultiple scales of roughness.

Adhesion of surfaces with wavy roughness and a shallow depression