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Numerically simulating deformations in thin elastic sheets is a challengingproblem in computational mechanics due to destabilizing compressive stressesthat result in wrinkling. Determining the location, structure, and evolution ofwrinkles in these problems have important implications in design and is an areaof increasing interest in the fields of physics and engineering. In this work,several numerical approaches previously proposed to model equilibriumdeformations in thin elastic sheets are compared. These include standard finiteelement-based static post-buckling approaches as well as a recently proposedmethod based on dynamic relaxation, which are applied to the problem of anannular sheet with opposed tractions where wrinkling is a key feature.Numerical solutions are compared to analytic predictions, enabling aquantitative evaluation of the predictive power of the various methods. Resultsindicate that static finite element approaches are highly sensitive to initialimperfections, relying on \textit{a priori} knowledge of the equilibriumwrinkling pattern to generate optimal results. In contrast, dynamic relaxationis much less sensitive to initial imperfections and can generate solutions fora wide variety of loading conditions without requiring knowledge of theequilibrium solution beforehand.

A comparative analysis of numerical approaches to the mechanics of elastic sheets