支持相场模型和弹塑性-粘塑性相变的统一 MPM 框架

IF 7.8 1区 计算机科学 Q1 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Zaili Tu, Chen Li, Zipeng Zhao, Long Liu, Chenhui Wang, Changbo Wang, Hong Qin
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引用次数: 0

摘要

近年来,针对流体、固体以及它们在计算机动画中的微妙耦合,许多基于物理的建模和仿真算法与技术得到了快速应用。然而,如何模拟流体-固体相变过程中复杂的弹性-粘弹性(EVP)行为,并促进它们在同一框架内的无缝互动,仍然是一个具有挑战性的问题。在本文中,我们提出了一种实用的方法,能够模拟颗粒流动、粘塑液体、弹塑固体、刚体以及它们之间的相互作用,支持大量涉及现实相变的新现象,包括溶解、熔化、冷却、膨胀、收缩等。在物理学层面,我们建议将 von Mises 与 Drucker-Prager 和 Cam-Clay 屈服模型相结合并进行变形,以建立统一的相场驱动 EVP 模型,该模型能够描述颗粒、弹性、塑性、粘性材料、液体、非牛顿流体的行为及其平滑演化。在数值层面,我们用材料点法(MPM)推导出了 Cahn-Hilliard 和 Allen-Cahn 方程的离散化形式,以有效跟踪相场演化,从而避免明确处理界面上的边界条件。在应用层面,我们设计了一种新颖的启发式策略,通过用户自定义方案(包括化学势、密度曲线等)来控制特殊行为。我们展示了大量具有挑战性的实验结果,以验证新的统一方法的有效性和通用性。这种灵活、高度稳定的框架建立在统一处理、各相之间的无缝耦合以及有效的数值离散化基础之上,在动画创作方面具有独特的优势,可以在艺术创造力和指导下创作出大量涉及相变的新现象。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Unified MPM Framework supporting Phase-field Models and Elastic-viscoplastic Phase Transition

Recent years have witnessed the rapid deployment of numerous physics-based modeling and simulation algorithms and techniques for fluids, solids, and their delicate coupling in computer animation. However, it still remains a challenging problem to model the complex elastic-viscoplastic (EVP) behaviors during fluid-solid phase transitions and facilitate their seamless interactions inside the same framework. In this paper, we propose a practical method capable of simulating granular flows, viscoplastic liquids, elastic-plastic solids, rigid bodies, and interacting with each other, to support novel phenomena all heavily involving realistic phase transitions, including dissolution, melting, cooling, expansion, shrinking, etc. At the physics level, we propose to combine and morph von Mises with Drucker-Prager and Cam-Clay yield models to establish a unified phase-field-driven EVP model, capable of describing the behaviors of granular, elastic, plastic, viscous materials, liquid, non-Newtonian fluids, and their smooth evolution. At the numerical level, we derive the discretization form of Cahn-Hilliard and Allen-Cahn equations with the material point method (MPM) to effectively track the phase-field evolution, so as to avoid explicit handling of the boundary conditions at the interface. At the application level, we design a novel heuristic strategy to control specialized behaviors via user-defined schemes, including chemical potential, density curve, etc. We exhibit a set of numerous experimental results consisting of challenging scenarios in order to validate the effectiveness and versatility of the new unified approach. This flexible and highly stable framework, founded upon the unified treatment and seamless coupling among various phases, and effective numerical discretization, has its unique advantage in animation creation towards novel phenomena heavily involving phase transitions with artistic creativity and guidance.

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来源期刊
ACM Transactions on Graphics
ACM Transactions on Graphics 工程技术-计算机:软件工程
CiteScore
14.30
自引率
25.80%
发文量
193
审稿时长
12 months
期刊介绍: ACM Transactions on Graphics (TOG) is a peer-reviewed scientific journal that aims to disseminate the latest findings of note in the field of computer graphics. It has been published since 1982 by the Association for Computing Machinery. Starting in 2003, all papers accepted for presentation at the annual SIGGRAPH conference are printed in a special summer issue of the journal.
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