Why shear adhesion is not monotonically enhanced by stiffening

Interfaces between dissimilar elastic materials are ubiquitous in biological and engineered systems and often span orders of magnitude in stiffness. Yet it remains unclear whether stiffening an adhesive system strengthens or weakens shear adhesion, as conflicting trends have been widely reported and the underlying physics has remained unresolved. Here we provide a mechanistic explanation by developing a unified framework for shear adhesion across broad modulus contrasts. We derive an analytical solution for a finite-height elastic adhesive bonded to an elastic substrate and validate the theory using systematic experiments and finite element simulations. We show that, despite global shear loading for the typical geometries encountered, interfacial failure is governed by edge-initiated separation dominated by opening-mode fracture within a finite cohesive zone, rather than by interfacial sliding. Across more than six orders of magnitude in shear modulus contrast, shear adhesion exhibits a pronounced nonmonotonic dependence on stiffness, characterized by well-defined local maxima and minima that delineate attachment- and detachment-favorable regimes. This behavior arises from a competition between a modulus-contrast-dependent corner stress singularity, which promotes separation initiation, and elastic deformation, which controls interfacial opening. Building on this mechanism, we construct parameterized adhesion maps that identify optimal modulus ratios for robust attachment and on-demand release. These results reconcile disparate experimental observations by revealing their common physical origin, establish modulus contrast as an independent design variable for shear adhesion, and provide predictive guidelines for designing bioinspired, wearable, and robotic adhesive systems.