Isogeometric Analysis of Wrinkling
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ABSTRACT Wrinkling is a phenomenon that is omnipresent. Besides being well-known in the context of cosmetics, wrinkling of membranes is a structural instability studied in multiple disciplines. From nanometer scale, when studying the influence of wrinkles on the properties of graphene, to kilometer scale, when studying the influence of wrinkling on the structural stability of very large floating structures. From solar sails and space antennas in the aerospace domain, to the airspace for parachutes. From biomedical sciences studying wound healing to biological sciences studying brain morphology. My PhD thesis “Isogeometric Analysis of Wrinkling” [1] presents a computational model dedicated to the simulation of wrinkling phenomena in thin membranes. The model is based on the isogeometric Kirchhoff-Love shell model [2], justified by the low thickness of membranes and the importance of geometry and geometric non-linearities when considering wrinkling as a structural instability. On top of this shell theory, the developed model features hyperelastic constitutive models, duality-based goal-oriented error estimators and local mesh adaptivity, the construction of smooth splines over complex topologies and efficient schemes for load-stepping. The full model has been published as open-source code, and the thesis provides detailed instructions for result reproduction. In my presentation, I will introduce the problem of membrane wrinkling from a physical point of view and provide a brief overview of applications in different fields. Thereafter, I will highlight two unique features of the isogeometric membrane wrinkling model: (i) a simplified model to model wrinkling without modelling wrinkles [3], and, (ii) an adaptive parallel arc-length method for the parallelization of quasi-static simulations beyond the spatial dimensions [4]. I will conclude my talk with a set of directions for future research. REFERENCES [1] Verhelst, H. M. (2024). Isogeometric Analysis of Wrinkling. PhD Thesis, Delft University of Technology [2] Kiendl, J., Bletzinger, K. U., Linhard, J., & Wüchner, R. (2009). Isogeometric shell analysis with Kirchhoff–Love elements. Computer methods in applied mechanics and engineering, 198(49-52), 3902-3914. [3] Verhelst, H. M., Möller, M., & Den Besten, J. H. (2025). A wrinkling model for general hyperelastic materials based on tension field theory. Computer Methods in Applied Mechanics and Engineering, 441, 117955. [4] Verhelst, H. M., Den Besten, J.