He Xiaowei, Wang Huamin, Wu Enhua
IEEE Trans Vis Comput Graph. 2018 Sep;24(9):2589-2599. doi: 10.1109/TVCG.2017.2755646. Epub 2017 Sep 22.
Unified simulation of versatile elastoplastic materials and different dimensions offers many advantages in animation production, contact handling, and hardware acceleration. The unstructured particle representation is particularly suitable for this task, thanks to its simplicity. However, previous meshless techniques either need too much computational cost for addressing stability issues, or lack physical meanings and fail to generate interesting deformation behaviors, such as the Poisson effect. In this paper, we study the development of an elastoplastic model under the state-based peridynamics framework, which uses integrals rather than partial derivatives in its formulation. To model elasticity, we propose a unique constitutive model and an efficient iterative simulator solved in a projective dynamics way. To handle plastic behaviors, we incorporate our simulator with the Drucker-Prager yield criterion and a reference position update scheme, both of which are implemented under peridynamics. Finally, we show how to strengthen the simulator by position-based constraints and spatially varying stiffness models, to achieve incompressibility, particle redistribution, cohesion, and friction effects in viscoelastic and granular flows. Our experiments demonstrate that our unified, meshless simulator is flexible, efficient, robust, and friendly with parallel computing.
通用弹塑性材料和不同维度的统一模拟在动画制作、接触处理和硬件加速方面具有诸多优势。非结构化粒子表示因其简单性而特别适合此任务。然而，先前的无网格技术要么为解决稳定性问题需要过多计算成本，要么缺乏物理意义且无法生成有趣的变形行为，如泊松效应。在本文中，我们研究基于状态的近场动力学框架下弹塑性模型的开发，该框架在其公式中使用积分而非偏导数。为了对弹性进行建模，我们提出了一个独特的本构模型和一个以投影动力学方式求解的高效迭代模拟器。为了处理塑性行为，我们将模拟器与德鲁克 - 普拉格屈服准则和参考位置更新方案相结合，这两者均在近场动力学下实现。最后，我们展示了如何通过基于位置的约束和空间变化的刚度模型来增强模拟器，以在粘弹性和颗粒流中实现不可压缩性、粒子重新分布、内聚和摩擦效应。我们的实验表明，我们统一的无网格模拟器灵活、高效、稳健且便于并行计算。
