Progressive Shell Quasistatics for Unstructured Meshes

Jiayi Eris Zhang1,2, Jérémie Dumas1, Yun (Raymond) Fei1, Alec Jacobson1,3, Doug L. James2, Danny M. Kaufman1

1Adobe Research, 2Stanford University, 3University of Toronto

ACM Transactions on Graphics (SIGGRAPH Asia 2023)
Dreaming of Progressive Shell Quasistatics (PSQ): Progressive simulation of sleepy shell characters resting inside a rigid fullerene shape. Both the rigid colliders (bunny and cage) and the balloon-like characters are modeled using unstructured meshes, which are coarsened, posed by an artist, and then progressively and safely refined (Left to Right) during PSQ simulation. (Left) Our fast, coarse-mesh PSQ approximation is an excellent predictor across simulation scales, and faithfully represents the (Middle) intermediate-resolution solution and the (Right, Far-Right) converged fine-scale solution complete with deformed character details and wrinkles. Despite these benefits, the coarse PSQ proxy is over two orders of magnitude faster to simulate than its detailed counterpart. Sweet dreams.



Thin shell structures exhibit complex behaviors critical for modeling and design across wide-ranging applications. Capturing their mechanical response requires finely detailed, high-resolution meshes. Corresponding simulations for predicting equilibria with these meshes are expensive, whereas coarse-mesh simulations can be fast but generate unacceptable artifacts and inaccuracies. The recently proposed progressive simulation framework [Zhang et al. 2022] offers a promising avenue to address these limitations with consistent and progressively improving simulation over a hierarchy of increasingly higher-resolution models. Unfortunately, it is currently severely limited in application to meshes and shapes generated via Loop subdivision.

We propose Progressive Shells Quasistatics to extend progressive simulation to the high-fidelity modeling and design of all input shell (and plate) geometries with unstructured (as well as structured) triangle meshes. To do so, we construct a fine-to-coarse hierarchy with a novel nonlinear prolongation operator custom-suited for curved-surface simulation that is rest-shape preserving, supports complex curved boundaries, and enables the reconstruction of detailed geometries from coarse-level meshes. Then, to enable convergent, high-quality solutions with robust contact handling, we propose a new, safe, and efficient shape-preserving upsampling method that ensures non-intersection and strain limits during refinement. With these core contributions, Progressive Shell Quasistatics enables, for the first time, wide generality for progressive simulation, including support for arbitrary curved-shell geometries, progressive collision objects, curved boundaries, and unstructured triangle meshes – all while ensuring that preview and final solutions remain free of intersections. We demonstrate these features across a wide range of stress tests where progressive simulation captures the wrinkling, folding, twisting, and buckling behaviors of frictionally contacting thin shells with orders-of-magnitude speed-up in examples over direct fine-resolution simulation.


  author = {Zhang, Jiayi Eris and Dumas, J\`{e}r\`{e}mie and Fei, Yun (Raymond) and Jacobson, Alec
  and James, Doug L. and Kaufman, Danny M.},
  title = {Progressive Shell Quasistatics for Unstructured Meshes},
  year = {2023},
  address = {New York, NY, USA},
  volume = {42},
  number = {6},
  journal = {ACM Trans. Graph.},
  articleno = {184},

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