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

TL;DR

This paper introduces a gradient-enhanced continuum model for cavitation in elastomers and adhesives, capturing the phase transition leading to cavity nucleation without pre-existing defects, and aligns well with experimental observations.

Contribution

It develops a thermodynamically consistent, material length scale-inclusive framework for cohesive instability, advancing understanding of cavity formation in soft materials.

Findings

Reproduces experimental cavity aspect ratio transitions

Shows strain stiffening and softening models exhibit cavitation-like instability

Provides a basis for integrating damage and fracture models

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.