  Position-based Dynamics (PBD) and its extension, eXtended Position-based
Dynamics (XPBD), have been predominantly applied to compliant constrained
dynamics, with their potential in finite strain inelasticity remaining
underexplored. XPBD stands in contrast to other meshless methods, such as the
Material Point Method (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 generally entails applying specific constraints, whether hard or
compliant, to collections of point masses. This paper revisits this perception,
investigating the potential of XPBD in handling inelastic materials that are
described with continuum mechanics based yield surfaces and elastoplastic flow
rules. Our inspiration is that a robust estimation of the velocity gradient is
key to effectively tracking deformation gradients in any meshless context. By
further incorporating implicit inelastic constitutive relationships, we
introduce an 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.
