Browsing by Author "Song, Sichen"

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    A NUMERICAL SCHEME AND VALIDATION OF THE ASYMPTOTIC ENERGY RELEASE RATE FORMULA FOR A 2D GEL THIN-FILM DEBONDING PROBLEM
    (2024) Calderer, Maria carme; Henao, Duvan; Sanchez, Manuel a.; Siegel, Ronald a.; Song, Sichen
    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.
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    Experiments, Modelling, and Simulations for a Gel Bonded to a Rigid Substrate
    (2023) Song, Sichen; Siegel, Ronald A.; Sanchez, Manuel A.; Carme Calderer, M.; Henao, Duvan
    In preparation for a more thorough study based on our own experimental work of the debonding of a thin film gel by stress concentration on the interface with a rigid substrate, in this article we revisit, from the viewpoint of the synergy between mathematics, experiments, and finite element simulations, the problem of the swelling of a thin rectangular polyacrylamide gel covalently bonded on the bottom surface to a glass slide. With methods of the calculus of variations and perturbation theory we show that the solution to the corresponding zero-displacement boundary value problem converges, in the thin film limit, to a uniquely defined uniform uniaxial extension on the direction normal to the substrate. Both the experiments and the finite element simulations that we perform confirm that the amount of lateral swelling is very small, with a very good quantitative agreement between the two approaches. The proposed model of minimizing an energy functional comprising both a term for the elastic distortion and the Flory-Huggins expression for the entropy of mixing is thus experimentally and numerically validated, with parameters coming from experimental measurements, including the initial polymer volume fraction of the hydrogel synthesized in the laboratory (which is taken as the reference configuration instead of the dry polymer).
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    Gels: Energetics, Singularities, and Cavitation
    (2024) Calderer, M. Carme; Henao, Duvan; Sanchez, Manuel A.; Siegel, Ronald A.; Song, Sichen
    This article studies equilibrium singular configurations of gels and addresses open questions concerning gel energetics. We model a gel as an incompressible, immiscible and saturated mixture of a solid polymer and a solvent that sustain chemical interactions at the molecular level. We assume that the energy of the gel consists of the elastic energy of its polymer network plus the Flory-Huggins energy of mixing. The latter involves the entropic energies of the individual components plus that of interaction between polymer and solvent, with the temperature dependent Flory parameter, ?, encoding properties of the solvent. In particular, a good solvent promoting the mixing regime, is found below the threshold value ? = 0.5, whereas the phase separating regime develops above that critical value. We show that cavities and singularities develop in the latter regime. We find two main classes of singularities: (i) drying out of the solvent, with water possibly exiting the gel domain through the boundary, leaving behind a core of exposed polymer at the centre of the gel; (ii) cavitation, in response to traction on the boundary or some form of negative pressure, with a cavity that can be either void or flooded by the solvent. The straightforward and unified mathematical approach to treat all such singularities is based on the construction of appropriate test functions, inspired by the particular states of uniform swelling or compression. The last topic of the article addresses a statistical mechanics rooted controversy in the research community, providing an experimental and analytic study in support of the phantom elastic energy versus the affine one.