Abstract
Contact of elastic solids with heterogeneous interface energy of adhesion is considered. The known results on the asymptotic analysis of the quasi-static crack propagation along with the Griffith-type approach (based on the energy balance) and the Irwin-type approach (based on the concept of the contact stress intensity factor) are applied to generalize the Johnson–Kendall–Roberts (JKR) theory of adhesive contact. Under the assumption of slightly heterogeneous adhesion, the effective interface energy is determined depending on the approach used. The asymptotic equivalence between the three derived models, including that based on the mixed Griffith–Irwin-type approach, has been established. The leading-order asymptotic approximation for the pull-off force is derived. The cases of the ray-shaped and periodically-patterned adhesion are considered in detail.
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