XPBI: Position-Based Dynamics with Smoothing Kernels Handles Continuum Inelasticity

TL;DR

This paper extends XPBD, a position-based dynamics method, to simulate inelastic and elastoplastic materials by incorporating continuum mechanics principles, enabling realistic real-time simulations of complex substances.

Contribution

It introduces a plasticity in-the-loop augmentation to XPBD, allowing accurate simulation of elastoplastic, viscoplastic, and granular materials using standard constitutive laws.

Findings

Effective simulation of snow, sand, and plasticine.

Integration with cloth and water simulations.

High-resolution, real-time performance.

Abstract

PBD and its extension, XPBD, have been predominantly applied to compliant constrained elastodynamics, with their potential in finite strain (visco-) elastoplasticity remaining underexplored. XPBD is often perceived to stand in contrast to other meshless methods, such as the MPM. MPM is based on discretizing the weak form of governing partial differential equations within a continuum domain, coupled with a hybrid Lagrangian-Eulerian method for tracking deformation gradients. In contrast, XPBD formulates specific constraints, whether hard or compliant, to positional degrees of freedom. We revisit this perception by investigating the potential of XPBD in handling inelastic materials that are described with classical continuum mechanics-based yield surfaces and elastoplastic flow rules. Our inspiration is that a robust estimation of the velocity gradient is a sufficiently useful key to effectively tracking deformation gradients in XPBD simulations. By further incorporating implicit inelastic constitutive relationships, we introduce a plasticity in-the-loop updated Lagrangian augmentation to XPBD. This enhancement enables the simulation of elastoplastic, viscoplastic, and granular substances following their standard constitutive laws. We demonstrate the effectiveness of our method through high-resolution and real-time simulations of diverse materials such as snow, sand, and plasticine, and its integration with standard XPBD simulations of cloth and water.