Song, Sichen2023-11-282023-11-282023-04https://hdl.handle.net/11299/258611University of Minnesota M.S. thesis. April 2023. Major: Mathematics. Advisor: Maria-Carme Calderer. 1 computer file (PDF); iii, 47 pages.The purpose of this thesis is to study debonding of a thin film gel induced by stress concentration on the interface with a rigid substrate, which is useful in medical device design. Using polyacrylamide gel as a model system, the configuration of a thin rectangular polyacrylamide gel covalently bonded on the top surface to a glass substrate after reaching swelling equilibrium is investigated by experiment, mathematical modeling, and finite element simulation. Using the calculus of variations and perturbation theory, we show that the solution to the appropriate zero-displacement boundary value problem converges, in the thin film limit, to a uniquely defined uniform uniaxial extension in 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 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 free energy of mixing is thus experimentally and numerically validated, with parameters obtained from experimental measurements, including the initial polymer volume fraction of the gel synthesized in the laboratory, which is taken as the reference configuration instead of dry polymer.enThesis or Dissertation