  The functionality of soft interfaces is crucial to many applications in
biology and surface science. Recent studies have used liquid drops to probe the
surface mechanics of elastomeric networks. Experiments suggest an intricate
surface elasticity, also known as the Shuttleworth effect, where surface
tension is not constant but depends on substrate deformation. However,
interpretations have remained controversial due to singular elastic
deformations, induced exactly at the point where the droplet pulls the network.
Here we reveal the nature of the elastocapillary singularity on a hyperelastic
substrate with various constitutive relations for the interfacial energy.
First, we finely resolve the vicinity of the singularity using goal-adaptive
finite element simulations. This confirms the universal validity, also at large
elastic deformations, of the previously disputed Neumann's law for the contact
angles. Subsequently, we derive exact solutions of nonlinear elasticity that
describe the singularity analytically. These solutions are in perfect agreement
with numerics, and show that the stretch at the contact line, as previously
measured experimentally, consistently points to a strong Shuttleworth effect.
Finally, using Noether's theorem we provide a quantitative link between wetting
hysteresis and Eshelby-like forces, and thereby offer a complete framework for
soft wetting in the presence of the Shuttleworth effect.
