In this paper, we present a unified framework to simulate non-Newtonian behaviors. We combine viscous and elasto-plastic stress into a unified particle solver to achieve various non-Newtonian behaviors ranging from fluid-like to solid-like. Our constitutive model is based on a Generalized Maxwell model, which incorporates viscosity, elasticity and plasticity in one non-linear framework by a unified way. On the one hand, taking advantage of the viscous term, we construct a series of strain-rate dependent models for classical non-Newtonian behaviors such as shear-thickening, shear-thinning, Bingham plastic, etc. On the other hand, benefiting from the elasto-plastic model, we empower our framework with the ability to simulate solid-like non-Newtonian behaviors, i.e., visco-elasticity/plasticity. In addition, we enrich our method with a heat diffusion model to make our method flexible in simulating phase change. Through sufficient experiments, we demonstrate a wide range of non-Newtonian behaviors ranging from viscous fluid to deformable objects. We believe this non-Newtonian model will enhance the realism of physically-based animation, which has great potential for computer graphics.

翻译：本文提出了一种模拟非牛顿行为的统一框架。我们将黏性应力与弹塑性应力结合到统一的粒子解算器中，以实现从类流体到类固体的多种非牛顿行为。本构模型基于广义麦克斯韦模型，通过统一方式将黏性、弹性与塑性整合进单一非线性框架。一方面，利用黏性项构造了一系列应变率依赖模型，用于描述经典非牛顿行为（如剪切增稠、剪切稀化、宾汉塑性等）；另一方面，借助弹塑性模型，赋予框架模拟类固体非牛顿行为（即黏弹塑性）的能力。此外，我们通过引入热扩散模型增强了方法的灵活性，使其能够模拟相变过程。通过充分的实验，我们展示了从黏性流体到可变形物体的广泛非牛顿行为。我们相信，该非牛顿模型将增强基于物理的动画的真实感，在计算机图形学领域具有广阔应用前景。