To understand the complex biomechanical mechanisms that cause polyp formation in soft biological tissues, we performed an analysis of a relatively simple, prototypical example of wrinkling of a growing thin ring (film) on a soft viscoelastic substrate. We addressed this example in the FEniCS programming environment, which also includes basic algorithms for solving partial differential equations, such as the Newton-Raphson method. Based on the simulations performed, we found that the number of wrinkles, and consequently the number of resulting polyps, is influenced by the film's thickness, its inner radius, and the stiffness ratio between the substrate and the film. In some cases, however, we observed unexpected deformation shapes that cannot be easily predicted. These arise from unexplained jumps in the system, which are a consequence of the system's nonlinear nature due to its geometry and the nonlinear material model of soft tissues.
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