A moving least square reproducing kernel particle method for unified multiphase continuum simulation

In physically based-based animation, pure particle methods are popular due to their simple data structure, easy implementation, and convenient parallelization. As a pure particle-based method and using Galerkin discretization, the Moving Least Square Reproducing Kernel Method (MLSRK) was developed in engineering computation as a general numerical tool for solving PDEs. The basic idea of Moving Least Square (MLS) has also been used in computer graphics to estimate deformation gradient for deformable solids. Based on these previous studies, we propose a multiphase MLSRK framework that animates complex and coupled fluids and solids in a unified manner. Specifically, we use the Cauchy momentum equation and phase field model to uniformly capture the momentum balance and phase evolution/interaction in a multiphase system, and systematically formulate the MLSRK discretization to support general multiphase constitutive models. A series of animation examples are presented to demonstrate the performance of our new multiphase MLSRK framework, including hyperelastic, elastoplastic, viscous, fracturing and multiphase coupling behaviours etc

A practical method for animating anisotropic elastoplastic materials

This paper introduces a simple method for simulating highly anisotropic elastoplastic material behaviors like the dissolution of fibrous phenomena (splintering wood, shredding bales of hay) and materials composed of large numbers of irregularly‐shaped bodies (piles of twigs, pencils, or cards). We introduce a simple transformation of the anisotropic problem into an equivalent isotropic one, and we solve this new “fictitious” isotropic problem using an existing simulator based on the material point method. Our approach results in minimal changes to existing simulators, and it allows us to re‐use popular isotropic plasticity models like the Drucker‐Prager yield criterion instead of inventing new anisotropic plasticity models for every phenomenon we wish to simulate

MPM based simulation for various solid deformation

Solid materials are responsible for many interesting phenomena. There are various types of them such as deformable objects and granular materials. In this paper, we present an MPM based framework to simulate the wide range of solid materials. In this framework, solid mechanics is based on the elastoplastic model, where we use von Mises criterion for deformable objects, and the Drucker-Prager model with non-associated plastic flow rules for granular materials. As a result, we can simulate different kinds of deformation of deformable objects and sloping failure for granular materials

Hybrid continuum-discrete simulation of granular impact dynamics

Granular impact -- the dynamic intrusion of solid objects into granular media -- is widespread across scientific and engineering applications including geotechnics. Existing approaches for simulating granular impact dynamics have relied on either a pure discrete method or a pure continuum method. Neither of these methods, however, is deemed optimal from the computational perspective. Here, we introduce a hybrid continuum-discrete approach, built on the coupled material-point and discrete-element method (MP-DEM), for simulating granular impact dynamics with unparalleled efficiency. To accommodate highly complex solid-granular interactions, we enhance the existing MP-DEM formulation with three new ingredients: (i) a robust contact algorithm that couples the continuum and discrete parts without any interpenetration under extreme impact loads, (ii) large deformation kinematics employing multiplicative elastoplasticity, and (iii) a trans-phase constitutive relation capturing gasification of granular media. For validation, we also generate experimental data through laboratory measurement of the impact dynamics of solid spheres dropped onto dry sand. Simulation of the experiments shows that the proposed approach can well reproduce granular impact dynamics in terms of impact forces, intrusion depths, and splash patterns. Further, through parameter studies on material properties, model formulations, and numerical schemes, we identify key factors for successful continuum-discrete simulation of granular impact dynamics

Neural Stress Fields for Reduced-order Elastoplasticity and Fracture

We propose a hybrid neural network and physics framework for reduced-order modeling of elastoplasticity and fracture. State-of-the-art scientific computing models like the Material Point Method (MPM) faithfully simulate large-deformation elastoplasticity and fracture mechanics. However, their long runtime and large memory consumption render them unsuitable for applications constrained by computation time and memory usage, e.g., virtual reality. To overcome these barriers, we propose a reduced-order framework. Our key innovation is training a low-dimensional manifold for the Kirchhoff stress field via an implicit neural representation. This low-dimensional neural stress field (NSF) enables efficient evaluations of stress values and, correspondingly, internal forces at arbitrary spatial locations. In addition, we also train neural deformation and affine fields to build low-dimensional manifolds for the deformation and affine momentum fields. These neural stress, deformation, and affine fields share the same low-dimensional latent space, which uniquely embeds the high-dimensional simulation state. After training, we run new simulations by evolving in this single latent space, which drastically reduces the computation time and memory consumption. Our general continuum-mechanics-based reduced-order framework is applicable to any phenomena governed by the elastodynamics equation. To showcase the versatility of our framework, we simulate a wide range of material behaviors, including elastica, sand, metal, non-Newtonian fluids, fracture, contact, and collision. We demonstrate dimension reduction by up to 100,000X and time savings by up to 10X

Solid deformation by material point method

Solid materials are responsible for many interesting phenomena. There are various types of them, such as deformable objects and granular materials. In this paper, we present an MPM based framework to simulate the wide range of solid materials. In this framework, solid mechanics is based on the elastoplastic model following small deformation theory. We use von Mises criterion for deformable objects, and the Drucker–Prager model with nonassociated plastic flow rules for granular materials. As a result, we can simulate different kinds of deformation of deformable objects and sloping failure for granular materials

A Unified Particle System Framework for Multi-Phase, Multi-Material Visual Simulations

We introduce a unified particle framework which integrates the phase-field method with multi-material simulation to allow modeling of both liquids and solids, as well as phase transitions between them. A simple elasto-plastic model is used to capture the behavior of various kinds of solids, including deformable bodies, granular materials, and cohesive soils. States of matter or phases, particularly liquids and solids, are modeled using the non-conservative Allen-Cahn equation. In contrast, materials---made of different substances---are advected by the conservative Cahn-Hilliard equation. The distributions of phases and materials are represented by a phase variable and a concentration variable, respectively, allowing us to represent commonly observed fluid-solid interactions. Our multi-phase, multi-material system is governed by a unified Helmholtz free energy density. This framework provides the first method in computer graphics capable of modeling a continuous interface between phases. It is versatile and can be readily used in many scenarios that are challenging to simulate. Examples are provided to demonstrate the capabilities and effectiveness of this approach

Towards a predictive multi-phase model for alpine mass movements and process cascades

Alpine mass movements can generate process cascades involving different materials including rock, ice, snow, and water. Numerical modelling is an essential tool for the quantification of natural hazards. Yet, state-of-the-art operational models are based on parameter back-calculation and thus reach their limits when facing unprecedented or complex events. Here, we advance our predictive capabilities for mass movements and process cascades on the basis of a three-dimensional numerical model, coupling fundamental conservation laws to finite strain elastoplasticity. In this framework, model parameters have a true physical meaning and can be evaluated from material testing, thus conferring to the model a strong predictive nature. Through its hybrid Eulerian–Lagrangian character, our approach naturally reproduces fractures and collisions, erosion/deposition phenomena, and multi-phase interactions, which finally grant accurate simulations of complex dynamics. Four benchmark simulations demonstrate the physical detail of the model and its applicability to real-world full-scale events, including various materials and ranging through five orders of magnitude in volume. In the future, our model can support risk-management strategies through predictions of the impact of potentially catastrophic cascading mass movements at vulnerable sites

ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics

Physical simulators have been widely used in robot planning and control. Among them, differentiable simulators are particularly favored, as they can be incorporated into gradient-based optimization algorithms that are efficient in solving inverse problems such as optimal control and motion planning. Simulating deformable objects is, however, more challenging compared to rigid body dynamics. The underlying physical laws of deformable objects are more complex, and the resulting systems have orders of magnitude more degrees of freedom and therefore they are significantly more computationally expensive to simulate. Computing gradients with respect to physical design or controller parameters is typically even more computationally challenging. In this paper, we propose a real-time, differentiable hybrid Lagrangian-Eulerian physical simulator for deformable objects, ChainQueen, based on the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM can simulate deformable objects including contact and can be seamlessly incorporated into inference, control and co-design systems. We demonstrate that our simulator achieves high precision in both forward simulation and backward gradient computation. We have successfully employed it in a diverse set of control tasks for soft robots, including problems with nearly 3,000 decision variables.Comment: In submission to ICRA 2019. Supplemental Video: https://www.youtube.com/watch?v=4IWD4iGIsB4 Project Page: https://github.com/yuanming-hu/ChainQuee

A Material Point Method for Simulating Frictional Contact with Diverse Materials

We present an extension to the Material Point Method (MPM) for simulating elastic objects with various co-dimensions like hair (1D), thin shells (2D), and volumetric objects (3D). We simulate thin shells with frictional contact using a combination of MPM and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Furthermore our technique naturally couples with other traditional MPM methods for simulating granular materials. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high resolution examples. For the simulation of hair and volumetric elastic objects, we utilize a Lagrangian mesh for internal force computation and an Eulerian mesh for self collision as well as coupling with external materials. While the updated Lagrangian discretization where the Eulerian grid degrees of freedom are used to take variations of the potential energy is effective in simulating thin shells, its frictional contact response strategy does not generalize to volumetric objects. Therefore, we develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM. 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