A pseudo-elastic model of underwater adhesive

Underwater adhesion remains a major challenge because water inhibits intimate contact between adhesive materials and submerged surfaces. Inspired by marine organisms that employ liquid-liquid phase separation for wet adhesion, we investigate the mechanical behavior of a silk fibroin-tannic acid viscoelastic coacervate. This water-immiscible material can exchange water with its surroundings, enabling the displacement of hydration layers at submerged interfaces. Its temperature-dependent behavior allows it to transition from a rigid state at low temperature to a soft, adhesive state at ambient conditions, facilitating spreading and bond formation underwater. Hydrostatic loading-unloading experiments reveal pronounced inelastic behavior characterized by stiffness reduction during hydrostatic tensile loading, stress softening upon unloading, and the accumulation of residual volumetric deformation. To describe these effects, we adapt the theory of pseudo-elasticity originally developed for the Mullins effect in rubber-like materials. Two internal variables are introduced to represent volumetric softening and residual deformation. The resulting constitutive model captures the observed stress softening, residual deformation, and the recovery during subsequent hydrostatic compression. Numerical results are shown to be in good agreement with experimental observations, demonstrating the ability of the proposed model to describe the inelastic volumetric response of this bio-inspired underwater adhesive.