Abstract: We present methods for the efficient simulation of various types of deformable bodies by using non‑deformation as a measure for model reduction. Our algorithm identifies nondeforming elements as those with low strain rates over multiple frames. We use adaptive rigidification as a tool to create approximation methods for the simulation of deformable bodies. We first use the method in the context of soft bodies, yielding simulations often orders of magnitude faster than the elastic simulations. Moreover, we present an oracle that allows rigidified elements to become elastic again as needed. Then, we adapt our method to thin shell models and tackle their respective challenges. Namely, we present how to handle rigidifying bending elements and an edge filter to improve the elastification oracle on contacts that cause bending deformation. Additionally, we measure the impact of numerical scaling on the conditioning of our system. We also present a fundamentally different view of rigidification, where we generate a sequence of resolutions with rigid patterns for an iterative multi‑layer method in constraint‑based approaches. In this last contribution, we aim to find the ground truth solution through a fast solver, rather than only generating visually consistent simulations. We demonstrate our results on various examples in 2D or 3D. We also dive into the implementation of the algorithms.
Authors
Alexandre Mercier-Aubin
Bibtex
@phdthesis{AlexMA_PhD,
author={Mercier-Aubin, Alexandre},
title={Adaptive Methods for Elastic Deformation},
year={2024},
opturl={TODO once it is added to the mcgill library},
school={McGill University}
}