Constrained projective dynamics

Abstract

This paper proposes a novel energy-momentum conserving integration method. Adopting Projective Dynamics, the proposed method extends its unconstrained minimization for time integration into the constrained form with the position-based energy-momentum constraints. This resolves the well-known problem of unwanted dissipation of energy and momenta without compromising the real-time performance and simulation stability. The proposed method also enables users to directly control the energy and momenta so as to easily create the vivid deformable and global motions they want, which is a fascinating feature for many real-time applications such as virtual/augmented reality and games.

An Optimization‐based SPH Solver for Simulation of Hyperelastic Solids

“…One well‐known issue is the artificial damping of the elastic energy. As discussed in the previous studies [DLK18; KUJH21], investigating energy‐momentum conserving schemes such as constrained optimization, Implicit‐Midpoint, and Newmark‐beta remains as a future work.…”

Momentum‐preserving inversion alleviation for elastic material simulation

“…To address the dissipation, Dinev et al 14 propose FEPR, which enforced energy‐momentum conservation as a post‐processing procedure of an arbitrary solver. Kee et al 15 proposed an energy‐momentum conserving integration method based on PD. While they tackled momentum conservation of numerical solvers, our method targets alleviating inversions aiming at momentum conservation in the alleviated state.…”