- Number
- 10019827
- Published
- 2018-07-10
- Filed
- 2014-04-21
- Assignee
- Disney Enterprises, Inc.
- Inventors
- Selle; Andrew; Chai; Lawrence; Stomakhin; Alexey; Teran; Joseph
- CPC
- G06T13/60; G06F30/20
- Verdict
- Medium Notable software
- Source
- Google Patents · FreePatentsOnline
The keeper's note
Material-point-method granular physics simulation.
Abstract
The disclosure provides an approach for simulating and rendering granular materials. A simulation application generates video frames depicting a granular material phenomenon using a strain based elasto-plastic constitutive model integrated with a hybrid Eulerian/Lagrangian material point method (MPM). The elasto-plastic constitutive model includes physical equation(s) which dictate forces that affect the granular material during the simulation. In particular, the constitutive model may include user-controllable parameters defining threshold(s) to start plastic deformation, as well as a hardening parameter which controls how fast the granular material packs under compression. The MPM is a procedure in which particles of the granular material and a background grid are coupled, with the grid being used to assist in computing forces dictated by the physical equation(s) of the elasto-plastic constitutive model. In one configuration, the grid may further be rendered with volumetric rendering to generate video frames depicting the granular material.
Background
BACKGROUND(1) Field(2) This disclosure provides techniques for simulating and rendering granular materials. More specifically, aspects of this disclosure present a material point method for simulation of granular materials.(3) Description of the Related Art(4) In physics engines, “solvers” are used to simulate physical behavior of objects (e.g., the physical response of an object to a collision with another object). These solvers typically employ numerical techniques to approximate the physics so that simulations can be efficiently performed on a computer. Specialized solvers have been used to simulate a variety of phenomena in graphics and computational physics. Such solvers include fluid simulators, rigid body simulators, and cloth simulators, among others, each of which is suited to simulating behavior of a particular type of material. For example, fluid simulators are suited for simulating liquids which deform with no memory, while rigid body simulators are suited for simulating destruction and debris where there is no deformation (e.g., glass shattering). When solids and fluids are needed simultaneously, two-way coupled systems have been used to obtain accuracy and performance for both phenomena.(5) Granular materials (e.g., snow, sand, dust, etc.) can have continuously varying phase effects, i.e., these materials sometimes behave as a rigid/deforming solid and sometimes as a fluid. Traditional solvers and coupled systems are unable to simultaneously handle a continuum o
Claims
1. A computer-implemented method for rendering a granular material, the method comprising: receiving states of particles of the granular material; rasterizing the states of the particles to a grid; computing, on the grid, forces dictated by an elasto-plastic constitutive model which factors into plastic strain and elastic strain using finite-strain multiplicative elasticity with the elasticity being hyperelastic, wherein: the elasto-plastic constitutive model is defined in terms of an elasto-plastic energy density function having form Ψ ( F E , F P ) = μ ( F P ) .Math. F E - R E .Math. F 2 + λ ( F P ) 2 ( J E - 1 ) 2 , F.sub.E being an elastic part and F.sub.p being a plastic part of a deformation gradient F, F.sub.E is given by a fixed corotated energy density, Lamé parameters in the elasto-plastic constitutive model are functions of plastic deformation gradients μ(F.sub.P)=μ.sub.0e.sup.ξ(1−J.sup.P.sup.) and λ(F.sub.P)=λ.sub.0e.sup.ξ(1−J.sup.P.sup.), and J.sub.E=detF.sub.E, J.sub.p=detF.sub.P, F.sub.E=R.sub.ES.sub.E by a polar decomposition, λ.sub.0 and μ.sub.0 are initial Lamé coefficients, and ξ is a dimensionless plastic hardening parameter; updating velocities on the grid based, at least in part, on the forces dictated by the elasto-plastic constitutive model; updating the states of the particles based, at least in part, on the updated velocities on the grid; and rendering one or more images of the granular material based, at least in part, on a rasterization of the updated states of the particles to the grid.
9. A non-transitory computer-readable storage medium storing a program, which, when executed by a processor performs operations for rendering a granular material, the operations comprising: receiving states of particles of the granular material; rasterizing the states of the particles to a grid; computing, on the grid, forces dictated by an elasto-plastic constitutive model which factors into plastic strain and elastic strain using finite-strain multiplicative elasticity with the elasticity being hyperelastic, wherein: the elasto-plastic constitutive model is defined in terms of an elasto-plastic energy density function having form Ψ ( F E , F P ) = μ ( F P ) .Math. F E - R E .Math. F 2 + λ ( F P ) 2 ( J E - 1 ) 2 , F.sub.E being an elastic part and F.sub.P being a plastic part of a deformation gradient F, F.sub.E is given by a fixed corotated energy density, Lamé parameters in the elasto-plastic constitutive model are functions of plastic deformation gradients μ(F.sub.P)=μ.sub.0e.sup.ξ(1−J.sup.P.sup.) and λ(F.sub.P)=λ.sub.0e.sup.ξ(1−J.sup.P.sup.), and J.sub.E=detF.sub.E, J.sub.p=detF.sub.p, F.sub.E=R.sub.ES.sub.E by a polar decomposition, λ.sub.0 and μ.sub.0 are initial Lamé coefficients, and ξ is a dimensionless plastic hardening parameter; updating velocities on the grid based, at least in part, on the forces dictated by the elasto-plastic constitutive model; updating the states of the particles based, at least in part, on the updated velocities on the grid; and rendering one or more images of the granular material based, at least in part, on a rasterization of the updated states of the particles to the grid.
17. A system, comprising: a processor; and a memory, wherein the memory includes an application program configured to perform operations for rendering a granular material, the operations comprising: receiving states of particles of the granular material, rasterizing the states of the particles to a grid, computing, on the grid, forces dictated by an elasto-plastic constitutive model which factors into plastic strain and elastic strain using finite-strain multiplicative elasticity with the elasticity being hyperelastic, wherein: the elasto-plastic constitutive model is defined in terms of an elasto-plastic energy density function having form Ψ ( F E , F P ) = μ ( F P ) .Math. F E - R E .Math. F 2 + λ ( F P ) 2 ( J E - 1 ) 2 , F.sub.E being an elastic part and F.sub.P being a plastic part of a deformation gradient F, F.sub.E is given by a fixed corotated energy density, Lamé parameters in the elasto-plastic constitutive model are functions of plastic deformation gradients μ(F.sub.P)=μ.sub.0e.sup.ξ(1−J.sup.P.sup.) and λ(F.sub.P)=λ.sub.0e.sup.ξ(1−J.sup.P.sup.), and J.sub.E=detF.sub.E, J.sub.p=detF.sub.p, F.sub.E=R.sub.ES.sub.E by a polar decomposition, μ.sub.0 and μ.sub.0 are initial Lamé coefficients, and ξ is a dimensionless plastic hardening parameter; updating velocities on the grid based, at least in part, on the forces dictated by the elasto-plastic constitutive model, updating the states of the particles based, at least in part, on the updated velocities on the grid, and rendering one or more images of the granular material based, at least in part, on a rasterization of the updated states of the particles to the grid.