Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control

Tassilo Kugelstadt, Jan Bender, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Fabian Löschner, Andreas Longva
Proceedings of the ACM on Computer Graphics and Interactive Techniques (Best Paper Award at SCA)

We develop a new operator splitting formulation for the simulation of corotated linearly elastic solids with Smoothed Particle Hydrodynamics (SPH). Based on the technique of Kugelstadt et al. [KKB2018] originally developed for the Finite Element Method (FEM), we split the elastic energy into two separate terms corresponding to stretching and volume conservation, and based on this principle, we design a splitting scheme compatible with SPH. The operator splitting scheme enables us to treat the two terms separately, and because the stretching forces lead to a stiffness matrix that is constant in time, we are able to prefactor the system matrix for the implicit integration step. Solid-solid contact and fluid-solid interaction is achieved through a unified pressure solve. We demonstrate more than an order of magnitude improvement in computation time compared to a state-of-the-art SPH simulator for elastic solids.

We further improve the stability and reliability of the simulation through several additional contributions. We introduce a new implicit penalty mechanism that suppresses zero-energy modes inherent in the SPH formulation for elastic solids, and present a new, physics-inspired sampling algorithm for generating high-quality particle distributions for the rest shape of an elastic solid. We finally also devise an efficient method for interpolating vertex positions of a high-resolution surface mesh based on the SPH particle positions for use in high-fidelity visualization.

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author = {Kugelstadt, Tassilo and Bender, Jan and Fern{\'{a}}ndez-Fern{\'{a}}ndez, Jos{\'{e}} Antonio and Jeske, Stefan Rhys and L{\"{o}}schner, Fabian and Longva, Andreas},
title = {Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control},
year = {2021},
issue_date = {September 2021},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {4},
number = {3},
url = {https://doi.org/10.1145/3480142},
doi = {10.1145/3480142},
journal = {Proc. ACM Comput. Graph. Interact. Tech.},
month = sep,
articleno = {33},
numpages = {21},
keywords = {Smoothed Particle Hydrodynamics, fluid simulation, deformable solids, solid-fluid coupling}

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