MPM In Computer Graphics: Up to November 2019

by Chenfanfu Jiang

Here I overview the appearance of the Material Point Method (MPM) in Computer Graphics literatures based on the order of time. Please email me at if you would like to point out a mistake or if I missed any paper. Note that pure incompressible fluid papers with a MAC grid + FLIP particles + Poisson pressure solve are not considered as MPM papers in this summary.

Summary (click to see abstract)


Hegemann, Jan, Chenfanfu Jiang, Craig Schroeder, and Joseph M. Teran. "A level set method for ductile fracture." In Proceedings of the 12th ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 193-201. ACM, 2013.

Stomakhin, Alexey, Craig Schroeder, Lawrence Chai, Joseph Teran, and Andrew Selle. "A material point method for snow simulation." ACM Transactions on Graphics (TOG) 32, no. 4 (2013): 102.


Stomakhin, Alexey, Craig Schroeder, Chenfanfu Jiang, Lawrence Chai, Joseph Teran, and Andrew Selle. "Augmented MPM for phase-change and varied materials." ACM Transactions on Graphics (TOG) 33, no. 4 (2014): 138.


Gast, Theodore F., Craig Schroeder, Alexey Stomakhin, Chenfanfu Jiang, and Joseph M. Teran. "Optimization integrator for large time steps." IEEE transactions on visualization and computer graphics 21, no. 10 (2015): 1103-1115.

Yue, Yonghao, Breannan Smith, Christopher Batty, Changxi Zheng, and Eitan Grinspun. "Continuum foam: A material point method for shear-dependent flows." ACM Transactions on Graphics (TOG) 34, no. 5 (2015): 160.

Ram, Daniel, Theodore Gast, Chenfanfu Jiang, Craig Schroeder, Alexey Stomakhin, Joseph Teran, and Pirouz Kavehpour. "A material point method for viscoelastic fluids, foams and sponges." In Proceedings of the 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 157-163. ACM, 2015.

Jiang, Chenfanfu, Craig Schroeder, Andrew Selle, Joseph Teran, and Alexey Stomakhin. "The affine particle-in-cell method." ACM Transactions on Graphics (TOG) 34, no. 4 (2015): 51.


Daviet, Gilles, and Florence Bertails-Descoubes. "A semi-implicit material point method for the continuum simulation of granular materials." ACM Transactions on Graphics (TOG) 35, no. 4 (2016): 102.

Klár, Gergely, Theodore Gast, Andre Pradhana, Chuyuan Fu, Craig Schroeder, Chenfanfu Jiang, and Joseph Teran. "Drucker-prager elastoplasticity for sand animation." ACM Transactions on Graphics (TOG) 35, no. 4 (2016): 103.

Jiang, Chenfanfu, Craig Schroeder, Joseph Teran, Alexey Stomakhin, and Andrew Selle. "The material point method for simulating continuum materials." In ACM SIGGRAPH 2016 Courses, p. 24. ACM, 2016.


Tampubolon, Andre Pradhana, Theodore Gast, Gergely Klár, Chuyuan Fu, Joseph Teran, Chenfanfu Jiang, and Ken Museth. "Multi-species simulation of porous sand and water mixtures." ACM Transactions on Graphics (TOG) 36, no. 4 (2017): 105.

Jiang, Chenfanfu, Theodore Gast, and Joseph Teran. "Anisotropic elastoplasticity for cloth, knit and hair frictional contact." ACM Transactions on Graphics (TOG) 36, no. 4 (2017): 152.

Klár, Gergely, Jeff Budsberg, Matt Titus, Stephen Jones, and Ken Museth. 2017. Production ready MPM simulations. In ACM SIGGRAPH 2017 Talks (SIGGRAPH '17). ACM, New York, NY, USA, Article 42, 2 pages. DOI:

Fu,Chuyuan, Qi Guo, Theodore Gast, Chenfanfu Jiang, and Joseph Teran. 2017. A polynomial particle-in-cell method. ACM Trans. Graph. 36, 6, Article 222 (November 2017), 12 pages. DOI:

Gao, Ming, Andre Pradhana Tampubolon, Chenfanfu Jiang, and Eftychios Sifakis. "An adaptive generalized interpolation material point method for simulating elastoplastic materials." ACM Transactions on Graphics (TOG) 36, no. 6 (2017): 223.

Wretborn, Joel, Rickard Armiento, and Ken Museth. "Animation of crack propagation by means of an extended multi-body solver for the material point method." Computers & Graphics 69 (2017): 131-13.9

Zhu, Fei, Jing Zhao, Sheng Li, Yong Tang, and Guoping Wang. "Dynamically enriched MPM for invertible elasticity." In Computer Graphics Forum, vol. 36, no. 6, pp. 381-392. 2017.


Gao, Ming, Andre Pradhana, Xuchen Han, Qi Guo, Grant Kot, Eftychios Sifakis, and Chenfanfu Jiang. "Animating fluid sediment mixture in particle-laden flows." ACM Transactions on Graphics (TOG) 37, no. 4 (2018): 149.

Guo, Qi, Xuchen Han, Chuyuan Fu, Theodore Gast, Rasmus Tamstorf, and Joseph Teran. "A material point method for thin shells with frictional contact." ACM Transactions on Graphics (TOG) 37, no. 4 (2018): 147.

Hu, Yuanming, Yu Fang, Ziheng Ge, Ziyin Qu, Yixin Zhu, Andre Pradhana, and Chenfanfu Jiang. "A moving least squares material point method with displacement discontinuity and two-way rigid body coupling." ACM Transactions on Graphics (TOG) 37, no. 4 (2018): 150.

Fei, Yun Raymond, Christopher Batty, Eitan Grinspun, and Changxi Zheng. "A multi-scale model for simulating liquid-fabric interactions." ACM Transactions on Graphics (TOG) 37, no. 4 (2018): 51.

Yan, Xiao. , Li, C. , Chen, X. and Hu, S. (2018), MPM simulation of interacting fluids and solids. Computer Graphics Forum, 37: 183-193. doi:10.1111/cgf.13523

Fang, Yu, Yuanming Hu, Shi‐Min Hu, and Chenfanfu Jiang. "A temporally adaptive material point method with regional time stepping." In Computer graphics forum, vol. 37, no. 8, pp. 195-204. 2018.

Gao, Ming, Xinlei Wang, Kui Wu, Andre Pradhana, Eftychios Sifakis, Cem Yuksel, and Chenfanfu Jiang. "Gpu optimization of material point methods." In SIGGRAPH Asia 2018 Technical Papers, p. 254. ACM, 2018.

Yue, Yonghao, Breannan Smith, Peter Yichen Chen, Maytee Chantharayukhonthorn, Ken Kamrin, and Eitan Grinspun. "Hybrid grains: adaptive coupling of discrete and continuum simulations of granular media." In SIGGRAPH Asia 2018 Technical Papers, p. 283. ACM, 2018.

Hu, Yuanming. "Taichi: An Open-Source Computer Graphics Library." arXiv preprint arXiv:1804.09293 (2018).


Ding, Ounan, and Schroeder Craig. "Penalty Force for Coupling Materials with Coulomb Friction." IEEE Transactions on Visualization & Computer Graphics 1 (2019): 1-1.

Wang, Stephanie, Mengyuan Ding, Theodore F. Gast, Leyi Zhu, Steven Gagniere, Chenfanfu Jiang, and Joseph M. Teran. "Simulation and Visualization of Ductile Fracture with the Material Point Method." Proceedings of the ACM on Computer Graphics and Interactive Techniques 2, no. 2 (2019): 18.

We present novel techniques for simulating and visualizing ductile fracture with the Material Point Method (MPM). We utilize traditional particle-based MPM [Stomakhin et al. 2013; Sulsky et al. 1994] as well as the Lagrangian energy formulation of [Jiang et al. 2015] that utilizes a tetrahedron mesh, rather than particle-based estimation of the deformation gradient and potential energy. We model failure and fracture via elastoplasticity with damage. Material is elastic until its deformation exceeds a Rankine or von Mises yield condition, at which point we use a softening model that shrinks the yield surface until a damage threshold is reached. Once damaged, the material Lamé coefficients are modified to represent failed material. We design visualization techniques for rendering the boundary of the material and its intersections with evolving crack surfaces. Our approach uses a simple and efficient element splitting strategy for tetrahedron meshes to represent crack surfaces that utilizes an extrapolation technique based on the MPM simulation. For traditional particle-based MPM we use an initial Delaunay tetrahedralization to connect randomly initialized MPM particles. Our visualization technique is a post-process and can be run after the MPM simulation for efficiency. We demonstrate our method with a number of challenging simulations of ductile failure with considerable and persistent self-contact.

Han, Xuchen, Theodore F. Gast, Qi Guo, Stephanie Wang, Chenfanfu Jiang, and Joseph Teran. "A Hybrid Material Point Method for Frictional Contact with Diverse Materials." Proceedings of the ACM on Computer Graphics and Interactive Techniques 2, no. 2 (2019): 17.

We present a new hybrid Lagrangian Material Point Method for simulating elastic objects like hair, rubber, and soft tissues that utilizes a Lagrangian mesh for internal force computation and an Eulerian mesh for self collision as well as coupling with external materials. While recent Material Point Method (MPM) techniques allow for natural simulation of hyperelastic materials represented with Lagrangian meshes, they utilize an updated Lagrangian discretization where the Eulerian grid degrees of freedom are used to take variations of the potential energy. This often coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts. We develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM, e.g. sand, snow, etc. Furthermore, while recent MPM advances allow for resolution of frictional contact with codimensional simulation of hyperelasticity, they do not generalize to the case of volumetric materials. We show that our hybrid approach resolves these issues. We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with multiple elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling.

Fang, Yu, Minchen Li, Ming Gao, and Chenfanfu Jiang. "Silly rubber: an implicit material point method for simulating non-equilibrated viscoelastic and elastoplastic solids." ACM Transactions on Graphics (TOG) 38, no. 4 (2019): 118.

Simulating viscoelastic polymers and polymeric fluids requires a robust and accurate capture of elasticity and viscosity. The computation is known to become very challenging under large deformations and high viscosity. Drawing inspirations from return mapping based elastoplasticity treatment for granular materials, we present a finite strain integration scheme for general viscoelastic solids under arbitrarily large deformation and non-equilibrated flow. Our scheme is based on a predictor-corrector exponential mapping scheme on the principal strains from the deformation gradient, which closely resembles the conventional treatment for elastoplasticity and allows straightforward implementation into any existing constitutive models. We develop a new Material Point Method that is fully implicit on both elasticity and inelasticity using augmented Lagrangian optimization with various preconditioning strategies for highly efficient time integration. Our method not only handles viscoelasticity but also supports existing elastoplastic models including Drucker-Prager and von-Mises in a unified manner. We demonstrate the efficacy of our framework on various examples showing intricate and characteristic inelastic dynamics with competitive performance.

Wolper, Joshuah, Yu Fang, Minchen Li, Jiecong Lu, Ming Gao, and Chenfanfu Jiang. "CD-MPM: continuum damage material point methods for dynamic fracture animation." ACM Transactions on Graphics (TOG) 38, no. 4 (2019): 119.

We present two new approaches for animating dynamic fracture involving large elastoplastic deformation. In contrast to traditional mesh-based techniques, where sharp discontinuity is introduced to split the continuum at crack surfaces, our methods are based on Continuum Damage Mechanics (CDM) with a variational energy-based formulation for crack evolution. Our first approach formulates the resulting dynamic material damage evolution with a Ginzburg-Landau type phase-field equation and discretizes it with the Material Point Method (MPM), resulting in a coupled momentum/damage solver rooted in phase field fracture: PFF-MPM. Although our PFF-MPM approach achieves convincing fracture with or without plasticity, we also introduce a return mapping algorithm that can be analytically solved for a wide range of general non-associated plasticity models, achieving more than two times speedup over traditional iterative approaches. To demonstrate the efficacy of the algorithm, we also develop a Non-Associated Cam-Clay (NACC) plasticity model with a novel fracture-friendly hardening scheme. Our NACC plasticity paired with traditional MPM composes a second approach to dynamic fracture, as it produces a breadth of organic, brittle material fracture effects on its own. Though NACC and PFF can be combined, we focus on exploring their material effects separately. Both methods can be easily integrated into any existing MPM solver, enabling the simulation of various fracturing materials with extremely high visual fidelity while requiring little additional computational overhead.

Nagasawa, Kentaro, Takayuki Suzuki, Ryohei Seto, Masato Okada, and Yonghao Yue. "Mixing sauces: a viscosity blending model for shear thinning fluids." ACM Transactions on Graphics (TOG) 38, no. 4 (2019): 95.

The materials around us usually exist as mixtures of constituents, each constituent with possibly a different elasto-viscoplastic property. How can we describe the material property of such a mixture is the core question of this paper. We propose a nonlinear blending model that can capture intriguing flowing behaviors that can differ from that of the individual constituents (Fig. 1). We used a laboratory device, rheometer, to measure the flowing properties of various fluid-like foods, and found that an elastic Herschel-Bulkley model has nice agreements with the measured data even for the mixtures of these foods. We then constructed a blending model such that it qualitatively agrees with the measurements and is closed in the parameter space of the elastic Herschel-Bulkley model. We provide validations through comparisons between the measured and estimated properties using our model, and comparisons between simulated examples and captured footages. We show the utility of our model for producing interesting behaviors of various mixtures.

Hu, Yuanming, Xinxin Zhang, Ming Gao, and Chenfanfu Jiang. "On hybrid lagrangian-eulerian simulation methods: practical notes and high-performance aspects." In ACM SIGGRAPH 2019 Courses, p. 16. ACM, 2019.

This course is focused on practical high-performance implementations of hybrid Lagrangian-Eulerian simulation schemes, especially the Material Point Method (MPM) and hybrid vortex methods. Starting with a gentle introduction to the schemes and modern computer architecture, we will cover topics including algorithmic design, data structures, parallelization, and low-level architecture-specific CPU/GPU optimizations.

Montazeri, Zahra, Chang Xiao, Yun Fei, Changxi Zheng, and Shuang Zhao. "Mechanics-Aware Modeling of Cloth Appearance." arXiv preprint arXiv:1904.11116 (2019).

Micro-appearance models have brought unprecedented fidelity and details to cloth rendering. Yet, these models neglect fabric mechanics: when a piece of cloth interacts with the environment, its yarn and fiber arrangement usually changes in response to external contact and tension forces. Since subtle changes of a fabric's microstructures can greatly affect its macroscopic appearance, mechanics-driven appearance variation of fabrics has been a phenomenon that remains to be captured. We introduce a mechanics-aware model that adapts the microstructures of cloth yarns in a physics-based manner. Our technique works on two distinct physical scales: using physics-based simulations of individual yarns, we capture the rearrangement of yarn-level structures in response to external forces. These yarn structures are further enriched to obtain appearance-driving fiber-level details. The cross-scale enrichment is made practical through a new parameter fitting algorithm for simulation, an augmented procedural yarn model coupled with a custom-design regression neural network. We train the network using a dataset generated by joint simulations at both the yarn and the fiber levels. Through several examples, we demonstrate that our model is capable of synthesizing photorealistic cloth appearance in a %dynamic and mechanically plausible way.

Zhao, Jianwang, Yi Chen, Haitong Zhang, Hao Xia, Zhangye Wang, and Qunsheng Peng. "Physically based modeling and animation of landslides with MPM." The Visual Computer (2019): 1-13.

Landslide is a disaster which may cause huge losses of human life and block the traffic on hilly area. In this paper, we present a new physically based model to simulate the dynamic flow of landslides, under a modified MPM (material point method) framework. To realistically simulate the characteristics of fracture and flow of soil medium in landslide, we introduce the modified Cambridge clay model (MCCM) from soil dynamics into the yield surface criterion to model the dynamic process of landslides. The interaction between soil and rock in the landslide is simulated by a level-set-based two-way fluid–solid coupling algorithm. Meanwhile, we propose a GPU-based optimization to calculate the signed distance function in level set to improve the efficiency of collision detection. We also simplify the hardening and softening parameter calculation algorithm of MCCM to reduce the calculation involved in landslide simulation. By choosing different values of the material yield surface parameters, various kinds of landslide disaster scenes with different cover area are successfully generated, including rocks rolling from hill, soil and rock collapsing, landslide flowing, and covering the road and cars. Experimental results demonstrate the potential of our method.

Fei, Yun Raymond, Christopher Batty, Eitan Grinspun, and Changxi Zheng. "A Multi-Scale Model for Coupling Strands with Shear-Dependent Liquid " SIGGRAPH Asia (2019)

We propose a framework for simulating the complex dynamics of strands interacting with compressible, shear-dependent liquids, such as oil paint, mud, cream, melted chocolate, and pasta sauce. Our framework contains three main components: the strands modeled as discrete rods, the bulk liquid represented as a continuum (material point method), and a reduced-dimensional flow of liquid on the surface of the strands with detailed elastoviscoplastic behavior. These three components are tightly coupled together. To enable discrete strands interacting with continuum-based liquid, we develop models that account for the volume change of the liquid as it passes through strands and the momentum exchange between the strands and the liquid. We also develop an extended constraint-based collision handling method that supports cohesion between strands. Furthermore, we present a principled method to preserve the total momentum of a strand and its surface flow, as well as an analytic plastic flow approach for Herschel-Bulkley fluid that enables stable semi-implicit integration at larger time steps. We explore a series of challenging scenarios, involving splashing, shaking, and agitating the liquid which causes the strands to stick together and become entangled.

Ding, Mengyuan, Xuchen Han, Stephanie Wang, Theodore Gast, Joseph Teran. "A Thermomechanical Material Point Method for Baking and Cooking" SIGGRAPH Asia (2019)

We present a Material Point Method for visual simulation of baking breads, cookies, pancakes and similar materials that consist of dough or batter (mixtures of water, flour, eggs, fat, sugar and leavening agents). We develop a novel thermomechanical model using mixture theory to resolve interactions between individual water, gas and dough species. Heat transfer with thermal expansion is used to model thermal variations in material properties. Water-based mass transfer is resolved through the porous mixture, gas represents carbon dioxide produced by leavening agents in the baking process and dough is modeled as a viscoelastoplastic solid to represent its varied and complex rheological properties. Water content in the mixture reduces during the baking process according to Fick's Law which contributes to drying and cracking of crust at the material boundary. Carbon dioxide gas produced by leavening agents during baking creates internal pressure that causes rising. The viscoelastoplastic model for the dough is temperature dependent and is used to model melting and solidification. We discretize the governing equations using a novel Material Point Method designed to track the solid phase of the mixture.

Hu, Yuanming, Tzu-Mao Li, Luke Anderson, Jonathan Ragan-Kelley, and Frédo Durand. "Taichi: a language for high-performance computation on spatially sparse data structures." ACM Transactions on Graphics (TOG) 38, no. 6 (2019): 201.

3D visual computing data are often spatially sparse. To exploit such sparsity, people have developed hierarchical sparse data structures, such as multi-level sparse voxel grids, particles, and 3D hash tables. However, developing and using these high-performance sparse data structures is challenging, due to their intrinsic complexity and overhead. We propose Taichi, a new data-oriented programming language for efficiently authoring, accessing, and maintaining such data structures. The language offers a high-level, data structure-agnostic interface for writing computation code. The user independently specifies the data structure. We provide several elementary components with different sparsity properties that can be arbitrarily composed to create a wide range of multi-level sparse data structures. This decoupling of data structures from computation makes it easy to experiment with different data structures without changing computation code, and allows users to write computation as if they are working with a dense array. Our compiler then uses the semantics of the data structure and index analysis to automatically optimize for locality, remove redundant operations for coherent accesses, maintain sparsity and memory allocations, and generate efficient parallel and vectorized instructions for CPUs and GPUs. Our approach yields competitive performance on common computational kernels such as stencil applications, neighbor lookups, and particle scattering. We demonstrate our language by implementing simulation, rendering, and vision tasks including a material point method simulation, finite element analysis, a multigrid Poisson solver for pressure projection, volumetric path tracing, and 3D convolution on sparse grids. Our computation-data structure decoupling allows us to quickly experiment with different data arrangements, and to develop high-performance data structures tailored for specific computational tasks. With 110 th as many lines of code, we achieve 4.55× higher performance on average, compared to hand-optimized reference implementations.