From cohesive to brittle debonding: the quasistatic framework

TL;DR

This paper demonstrates that in a quasistatic setting, solutions to cohesive debonding models with increasingly steep profiles converge to a brittle debonding limit, using a free-boundary reformulation.

Contribution

It introduces a rigorous framework showing the convergence of cohesive to brittle debonding models via energetic solutions and a free-boundary approach.

Findings

Convergence of cohesive to brittle debonding solutions established.

Validated the approximation of brittle laws with steep cohesive profiles.

Provided a new free-boundary reformulation for brittle debonding models.

Abstract

The approximation of brittle laws via steeper and steeper cohesive profiles is validated within the mechanical setting of debonding models, which describe the detachment process of a peeled elastic adhesive membrane. In a quasistatic framework, energetic solutions to a suitably rescaled cohesive debonding problem, formulated in terms of displacements, are proved to converge to a limit evolution of shapes solving its brittle counterpart. The proposed approach relies on an equivalent and recently introduced free-boundary reformulation of this latter model.