We present a model that combines the theories of Flory and Rehner of polymer swelling with nonlinear elasticity and Griffith’s fracture mechanics to study the debonding of gel membranes from rigid substrates. The model, validated through laboratory experiments, is motivated by the design of synthetic polymers that coat medical implants. A main goal is to analyze the energy release rate in order to determine the critical thickness below which the gel remains stable against debonding due to swelling-induced stresses. We investigate the ensuing Signorini and obstacle problems that constraint the membrane to remain above its substrate. We also discuss the case of a moving substrate, where the competition between shearing, adhesion and bending forces lead to the propagation of Schallamach waves in the film.
References:
Experiments and finite element simulations pertinent to hydrogel debonding from a solid substrate. M.Carme Calderer, D. Henao, Manuel Sanchez, Ronald A. Siegel and Sichen Song, Polymer, 335, 2025.
Debonding waves in gel thin films. Xianmin Xu, M.Carme Calderer, Masao Doi and Duvan Henao. Proc. Royal Soc. A, 476, 2020.
Gel Debonding from a Rigid Substrate. M. Carme Calderer, Carlos Garavito, Duvan Henao, Lorenzo Tapia and Suping Lyu. J. Elast. 141, 2020.
Experiments, Modelling, and Simulations for a Gel Bonded to a Rigid Substrate. Sichen Song, Ronald A. Siegel, Manuel A. Sánchez, M. Carme Calderer and Duvan Henao. J. Elast. 153, 2023.
A Numerical scheme and validation of the asymptotic energy release rate formula for a two-dimensional gel thin-film debonding problem. M. Carme Calderer, Duvan Henao, Manuel Sanchez, Ronald A. Siegel and Sichen Song. SIAM J. Appl. Math., 84, 2024.
Gels: Energetics, singularities, and cavitation. M.Carme Calderer, Duvan Henao, Manuel Sánchez, Ronald A. Siegel and Sichen Song. J. Elast. 2024.
Brandon Chabaud and M.Carme Calderer. Effects of permeability and viscosity in linear polymeric gels. Math. Meth. Appl. Sci. 39, 2016.
Giacomo Canevari, Università degli Studi di Verona