Modeling cavitation and fibrillation in elastomers and adhesives. Part I: Cohesive instability

Abstract

Cavitation in soft elastomers and adhesives is often viewed as an elastic instability, commonly tied to the study of incompressible solids. It is the first step prior to fibrillation and ultimate failure in adhesives. Building on the work of Lamont et al. (2025), elastomeric materials are treated as a crosslinked van der Waals fluid. The van der Waals contribution, capturing excluded volume and cohesive forces, is non-(poly)convex, readily providing an intrinsic analytical criterion for cavity nucleation. This work introduces a gradient-enhanced continuum framework that examines the emergence of cavity formation from the perspective of a cohesive instability and corresponding phase transition without requiring a pre-existing defect. The corresponding thermodynamically consistent derivation includes the introduction of a relevant material length scale as well as viscous dissipation associated with polymer chain disentanglement during the cohesive instability. This work does not study the impending damage that the material undergoes during the cohesive instability and transition from a dense to a rare phase. Interestingly, it is shown that for both strain stiffening and strain softening models (in terms of their shear response), an instability reminiscent of what is expected in the case of cavitation is recapitulated. Simulations reproduce key experimental trends, including the aspect ratio-driven transition from a few large to many small cavities depending on the thickness of an adhesive layer. The framework offers a robust, physically grounded basis for the cohesive instability that drives cavity nucleation, enabling future integration with damage, fracture, and dissipation models to capture the complete cavitation, fibrillation, and failure process.

Figures (20)

• Figure 1: Normalized bulk modulus considering $\mu=1$.
• Figure 2: Schematic of the Boundary Value Problems (BVPs) and loading conditions. (a) A constrained biaxial test under plane strain conditions. (b) A "pure shear" test under plane strain conditions.
• Figure 3: Macroscopic mechanical response of the square domain using the Neo-Hookean model. The red dashed line marks the analytical threshold ($J_{critical} \approx 1.15$) where the free energy loses convexity with respect to $J$. The red dots correspond to the field snapshots shown on top of the graph for steps 1, 80, 90, 100, 150, and 200.
• Figure 4: Sensitivity analysis of the Neo-Hookean model. (a) Effect of mesh refinement on the traction-volume response, showing convergence as the element size $h_e/H$ decreases from 0.1 to 0.025. (b) Influence of the viscosity of phase transition ($\eta$) on the onset of cavitation. Lower viscosity values result in a peak traction closer to the analytical instability threshold (red dashed line).
• Figure 5: Impact of mesh discretization (a) coarse and b) fine meshing) on the resolution of the cavity field.