A Numerical Scheme and Validation of the Asymptotic Energy Release Rate Formula for a 2D Gel Thin-Film Debonding Problem

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1766-1791, August 2024.
Abstract. This article presents a numerical scheme for the variational model formulated by Calderer et al. [J. Elast., 141 (2020), pp. 51–73] for the debonding of a hydrogel film from a rigid substrate upon exposure to solvent, in the two-dimensional case of a film placed between two parallel walls. It builds upon the scheme introduced by Song et al. [J. Elast., 153 (2023), pp. 651–679] for completely bonded gels, which fails to be robust in the case of gels that are already debonded. The new scheme is used to compute the energy release rate function, based on which predictions are offered for the threshold thickness below which the gel/substrate system is stable against debonding. This study, in turn, makes it possible to validate a theoretical estimate for the energy release rate obtained in the cited works, which is based on a thin-film asymptotic analysis and which, due to its explicit nature, is potentially valuable in medical device development. An existence theorem and rigorous justifications of some approximations made in our numerical scheme are also provided.