Mixed Variational Finite Elements for Implicit, General-Purpose Simulation of Deformables

TL;DR

This paper introduces a versatile mixed variational finite element method for implicit simulation of deformable objects, offering stability, efficiency, and broad applicability to various elastic models and geometries.

Contribution

It presents a new finite element approach using mixed variational principles that is stable, efficient, and adaptable to multiple elastic models and simulation domains.

Findings

Stable across a wide range of timestep sizes and material parameters

Efficient evaluation suitable for volume, surface, and rod models

Demonstrated effectiveness on diverse simulated examples

Abstract

We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating projections solver with a superset of the desirable properties of many previous fast solution strategies. This framework fits a range of elastic constitutive models and remains stable across a wide span of timestep sizes, material parameters (including problems that are quasi-static and approximately rigid). It is efficient to evaluate and easily applicable to volume, surface, and rods models. We demonstrate the efficacy of our approach on a number of simulated examples across all three codomains.