Second-Order Finite Elements for Deformable Surfaces

Published in ACM SIGGRAPH Asia 2023 Conference Proceedings, 2023

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Authors:
Qiqin Le, Yitong Deng, Jiamu Bu, Bo Zhu, Tao Du

Abstract:
We present a computational framework for simulating deformable surfaces with second-order triangular finite elements. Our method develops numerical schemes for discretizing stretching, shearing, and bending energies of deformable surfaces in a second-order finite-element setting. In particular, we introduce a novel discretization scheme for approximating mean curvatures on a curved triangle mesh. Our framework also integrates a virtual-node finite-element scheme that supports two-way coupling between cut-cell rods without expensive remeshing. We compare our approach with traditional simulation methods using linear and higher-order finite elements and demonstrate its advantages in several challenging settings, such as low-resolution meshes, anisotropic triangulation, and stiff materials. Finally, we showcase several applications of our framework in cloth simulation, mixed Origami and Kirigami, and biologically-inspired soft wing simulation.

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Acknowledgements:
Tao Du would like to thank Tsinghua University and Shanghai Qi Zhi Institute for supporting this research. Bo Zhu and Yitong Deng acknowledges the funding supports from NSF IIS-210673

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