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

Abstract
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. [2018] 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 highquality 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.
Description

        
@inproceedings{
10.1145:3480142
, booktitle = {
Proceedings of the ACM on Computer Graphics and Interactive Techniques
}, editor = {
Narain, Rahul and Neff, Michael and Zordan, Victor
}, title = {{
Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control
}}, author = {
Kugelstadt, Tassilo
and
Bender, Jan
and
Fernández-Fernández, José Antonio
and
Jeske, Stefan Rhys
and
Löschner, Fabian
and
Longva, Andreas
}, year = {
2021
}, publisher = {
ACM
}, ISSN = {
2577-6193
}, ISBN = {}, DOI = {
10.1145/3480142
} }
Citation