A Method for Animating Viscoelastic Fluids

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A Method for Animating Viscoelastic Fluids

• Tolga G. Goktekin Adam W. Bargteil James F.
  OBrien
• Presented by Yisheng Chen

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Viscoelastic

• Elastic
• s
• Viscous
• s
• Plastic
• Viscoelasticity is a generalization of elasticity
  and viscosity.

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Viscoelastic Fluids

• Initially respond to strain elastically like a
  solid, when subjected to increasingly large
  stresses they flow like a fluid
• mucus, egg white, clay, dough, gelatin, unset
  cement, liquid acrylic, toothpaste, gels,, and
  liquid soap

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Fluids, Solids, and the In-between

• Similarity
• Both resist changes to their volume
• Identical internal damping force for a solid and
  the viscous force for a fluid
• Distinction
• presence or absence of an elastic term that
  attempts to restore the material to its original
  shape
• Viscoelastic fluids or elastoplastic solids

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Background

• Carlson et al., 2002 opt to map the continuum
  between fluids and solids to varying viscosity. A
  solid is simply a fluid with very high viscosity
• Terzopoulos et al., 1989, Muller et al.,
  2003 particle-based methods for modeling highly
  viscous fluids and for modeling fluids with some
  form of elasticity w/o plasticity
• Terzopoulos et al., 1988, OBrien et al.,
  2002 limited amounts of plastic flow
• Navier-Stokes equations!

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Framework - Grid Foster and Fedkiw, 2001

• rectilinear grid that stores the values that
  define the fluids state (classic staggered MAC
  grid)
• crude voxelized approximation

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Framework - Levelset Enright et al., 2002
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Governing Equations

• modified version of the Navier-Stokes equations
  with an additional term for elastic stress
• omitting elastic and viscous terms relating to
  dilation

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Elastic, Plastic, and Total Strain

• no explicit deformation function available ? no
  derivatives to compute strain
• large deformation and flow experienced by the
  material ? impractical to track deformation
• compute strain by integrating strain rate

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• total, elastic and plastic strain

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Elastic Strain

• von Misess criterion for determining when
  plastic flow should occur Yielding occurs when
  the distortional energy density reaches a value
  equal to the distortional energy density at yield
  in a uniaxial case
• Elastic strain deviation
• limit is exceeded, flow occurs at a rate
  proportional to the amount the limit has been
  exceeded (r is the yield point)

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Grid Issues

• velocity components stored separately on faces
• strain tensor
• diagonal entries at the cell centers
• off-diagonal entries at the center of edges
  perpendicular to the component directions
• particle-level-set method for tracking the
  fluids free surface Enright et al., 2002
• susceptible to volume loss
• ameliorate the problem by using a level-set grid
  with twice the fluid grids resolution, and that
  is staggered with respect to the fluid grid

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Discussion

• Noticeable volume loss particularly when moving
  in orderly fashion, as opposed to splashing about
  chaotically
• A 403 grid 0.5h/s on a 3GHz P4 very high viscous
  or elastic coefficients would cause stability
  problems and force smaller time steps
• Materials only adhere to but no slip off
  boundaries surface components merge when collide
• A wide range of phenomena Biological fluids,
  simple polymer suspensions

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Liquid Representation

• The actual distribution of liquid is represented
  using an implicit surface. The implicit function
  is derived from a combination of inertialess
  particles and a dynamic isocontour.
• The isocontour provides a smooth surface to
  regions of liquid that are well resolved compared
  to our grid
• The particles provide detail where the surface
  starts to splash.

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Initialization of Particles

• Two sets of particles are randomly placed in a
  thickened surface region with positive
  particles in the f gt 0 region and negative
  particles in the fi lt0 region
• a particles location relative to the surface
  changes ? radius changes
• sp is the sign of the particle

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Hybrid Surface Model

• Level set volume loss near detailed features
• Particle -- visual artifacts when the number is
  small
• combination
• Particle velocity computed from the velocity grid
  using tri-linear interpolation
• Tracking f(x)0 using
• Delete or add particles according to update level
• Smooth region / high curvature / outside liquid
  surface