Modal Folding: Discovering Smooth Folding Patterns for Sheet Materials using Strain-Space Modes
<|reference_start|>Modal Folding: Discovering Smooth Folding Patterns for Sheet Materials using Strain-Space Modes: Folding can transform mundane objects such as napkins into stunning works of art. However, finding new folding transformations for sheet materials is a challenging problem that requires expertise and real-world experimentation. In this paper, we present Modal Folding -- an automated approach for discovering energetically optimal folding transformations, i.e., large deformations that require little mechanical work. For small deformations, minimizing internal energy for fixed displacement magnitudes leads to the well-known elastic eigenmodes. While linear modes provide promising directions for bending, they cannot capture the rotational motion required for folding. To overcome this limitation, we introduce strain-space modes -- nonlinear analogues of elastic eigenmodes that operate on per-element curvatures instead of vertices. Using strain-space modes to determine target curvatures for bending elements, we can generate complex nonlinear folding motions by simply minimizing the sheet's internal energy. Our modal folding approach offers a systematic and automated way to create complex designs. We demonstrate the effectiveness of our method with simulation results for a range of shapes and materials, and validate our designs with physical prototypes.<|reference_end|>
@article{tang2024modal,
    title={Modal Folding: Discovering Smooth Folding Patterns for Sheet Materials
  using Strain-Space Modes},
    author={Pengbin Tang, Ronan Hinchet, Roi Poranne, Bernhard Thomaszewski,
  Stelian Coros},
    journal={arXiv preprint arXiv:2405.04280},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.04280},
    primaryClass={cs.GR}
}