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

Position-based Dynamics (PBD) and its extension, eXtended Position-based Dynamics (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 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 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.