Micropolar Elasticity in Physically-Based Animation
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
ACM Association for Computing Machinery
Abstract
We explore micropolar materials for the simulation of volumetric deformable solids. In graphics, micropolar models have only been used in the form of one-dimensional Cosserat rods, where a rotating frame is attached to each material point on the one-dimensional centerline. By carrying this idea over to volumetric solids, every material point is associated with a microrotation, an independent degree of freedom that can be coupled to the displacement through a material’s strain energy density. The additional degrees of freedom give us more control over bending and torsion modes of a material. We propose a new orthotropic micropolar curvature energy that allows us to make materials stiff to bending in specific directions. For the simulation of dynamic micropolar deformables we propose a novel incremental potential formulation with a consistent FEM discretization that is well suited for the use in physically-based animation. This allows us to easily couple micropolar deformables with dynamic collisions through a contact model inspired from the Incremental Potential Contact (IPC) approach. For the spatial discretization with FEM we discuss the challenges related to the rotational degrees of freedom and propose a scheme based on the interpolation of angular velocities followed by quaternion time integration at the quadrature points. In our evaluation we validate the consistency and accuracy of our discretization approach and demonstrate several compelling use cases for micropolar materials. This includes explicit control over bending and torsion stiffness, deformation through prescription of a volumetric curvature field and robust interaction of micropolar deformables with dynamic collisions.
Description
CCS Concepts: Computing methodologies -> Physical simulation micropolar materials, cosserat continuum, elasticity, physically-based simulation, optimization time integration"
@inproceedings{10.1145:3606922,
booktitle = {Proceedings of the ACM on Computer Graphics and Interactive Techniques},
editor = {Wang, Huamin and Ye, Yuting and Victor Zordan},
title = {{Micropolar Elasticity in Physically-Based Animation}},
author = {Löschner, Fabian and Fernández-Fernández, José Antonio and Jeske, Stefan Rhys and Longva, Andreas and Bender, Jan},
year = {2023},
publisher = {ACM Association for Computing Machinery},
ISSN = {2577-6193},
ISBN = {},
DOI = {10.1145/3606922}
}