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.

翻译：摘要：基于位置的动力学（PBD）及其扩展——扩展型基于位置的动力学（XPBD），主要应用于柔性约束动力学领域，而其在有限应变非弹性问题中的潜力尚未被充分探索。XPBD与其他无网格方法（如物质点法MPM）形成鲜明对比。MPM基于连续介质域内控制偏微分方程弱形式的离散化，并结合混合拉格朗日-欧拉法追踪变形梯度。相比之下，XPBD通常对点质量集合施加特定约束（无论是刚性还是柔性）。本文重新审视这一认知，探究XPBD在处理基于连续介质力学屈服面与弹塑性流动法则描述的非弹性材料时的潜力。我们的灵感源于：在任何无网格背景下，速度梯度的稳健估计是有效追踪变形梯度的关键。通过进一步引入隐式非弹性本构关系，我们为XPBD提出了一种更新拉格朗日增强方法。该增强方法能够依照标准本构定律模拟弹塑性、粘塑性及颗粒状物质。我们通过高分辨率与实时仿真（涵盖雪、沙、橡皮泥等多种材料）验证了该方法的有效性，并将其与标准XPBD的布料与流体仿真进行了集成。