Quasi-Newton Methods for Real-time Simulation of Hyperelastic Materials


Tiantian Liu
University of Pennsylvania
 
Sofien Bouaziz
EPFL
 
Ladislav Kavan
University of Utah
 


Our method enables fast simulation of many different types of hyperelastic materials. Compared to the commonly-applied Newton's method, our method is about 10 times faster, while achieving even higher accuracy and being simpler to implement. The Polynomial and Spline-based materials are models recently introduced by Xu et al. [2015]. Spline-based material A is a modified Neo-Hookean material with stronger resistance to compression; spline-based material B is a modified Neo-Hookean material with stronger resistance to tension.



Abstract

We present a new method for real-time physics-based simulation supporting many different types of hyperelastic materials. Previous methods such as Position Based or Projective Dynamics are fast, but support only limited selection of materials; even classical materials such as the Neo-Hookean elasticity are not supported. Recently, Xu et al. [2015] introduced new "spline-based materials" which can be easily controlled by artists to achieve desired animation effects. Simulation of these types of materials currently relies on Newton's method, which is slow, even with only one iteration per timestep. In this paper, we show that Projective Dynamics can be interpreted as a quasi-Newton method. This insight enables very efficient simulation of a large class of hyperelastic materials, including the Neo-Hookean, spline-based materials, and others. The quasi-Newton interpretation also allows us to leverage ideas from numerical optimization. In particular, we show that our solver can be further accelerated using L-BFGS updates (Limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm). Our final method is typically more than 10 times faster than one iteration of Newton's method without compromising quality. In fact, our result is often more accurate than the result obtained with one iteration of Newton's method. Our method is also easier to implement, implying reduced software development costs.






Publication

Tiantian Liu, Sofien Bouaziz, Ladislav Kavan. Quasi-Newton Methods for Real-time Simulation of Hyperelastic Materials. ACM Transactions on Graphics 36(3) [Proceedings of SIGGRAPH],2017.    

Previously time-stamped on ArXiv as:
Tiantian Liu, Sofien Bouaziz, Ladislav Kavan. Towards Real-time Simulation of Hyperelastic Materials. arXiv, 2016.


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Acknowledgements

We thank Jernej Barbic, Erik Brunvand, Elaine Cohen, Sebastian Martin, James O'Brien, Mark Pauly, Peter Shirley, Cem Yuksel, and Hongyi Xu for many inspiring discussions. We also thank Petr Kadlecek for help with rendering, Dimitar Dinev for proofreading and Hannah Swan for narrating the accompanying video. This work was supported by NSF awards IIS-1622360 and IIS-1350330.