Is Griffith’ energetic criterion applicable to adhesive viscoelastic contacts?

Adhesion plays a key role in the mechanics of soft matter, where materials are highly deformable and viscoelastic. Classical adhesion theories originate from Griffith’s (1921) concept of crack equilibrium, which balances elastic energy release with the work of adhesion needed to form new surfaces. This principle was later adapted by Johnson, Kendall, and Roberts (1971), who treated the boundary of adhesive contact as equivalent to a Griffith crack. Although elegant, the energy balance framework is strictly valid only for elastic bodies. In viscoelastic systems, additional work must be performed against dissipative forces, motivating the introduction of an “effective work of adhesion,” as in the velocity-dependent models of Barquins and Maugis. However, these treatments remain largely empirical. This paper uses a more physically grounded understanding of adhesion in viscoelastic contacts, based on the scale separation of the processes of detachment and relaxation of material. As an example, the adhesive contact of a parabolic indenter and a viscoelastic half-space is analyzed across a wide range of pull-off velocities. The results show that the relationship between normal force and contact radius remains universal and velocity-independent, matching the JKR form; however, it exhibits a strongly increased effective work of adhesion. In contrast, the force–indentation response exhibits strong velocity dependence: at high detachment speeds, the contact separates at positive indentation depths within the indentation “well.”