Viscoelasticity

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Viscoelasticity
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Viscoelasticity

• While water and air are Newtonian, lots of other
  common stuff isnt
• Blood, paint, and many others have nonlinear
  viscosity (the faster these fluids deform, the
  less viscous it becomes)
• Silly putty, cornstarch in water (elastically
  resist fast changes, but flow eventually)
• Gels, pastes, dough (can hold a shape, but mixes
  like a fluid --- not quite a solid)
• Sand, powder, rubble (actually granular, but in
  bulk sometimes flow like fluids)

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Solids

• Lower down on the list the materials could be
  seen as solids with plasticity
• Plasticity permanent deformation flow
• The question becomes is the flowing part more
  important than the solid part?
• If so, might be worth simulating as a fluid with
  special solid-like properties

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Regular Viscoelasticity

• See Goktekin et al.04 and Irving06
• Idea add another fluid variable, elastic strain
  ?
• Encodes how much memory the fluid has of the
  state it wants to bounce back to
• Percent stretched or sheared in axis directions
• Include another fluid force, like pressure,
  proportional to elastic strain gradient
• Track elastic strain as it moves and rotates with
  the fluid, make it decay to zero (creep - silly
  putty) or clamp it to some range (like gels and
  pastes)

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Granular Materials

• Granular materials like sand are a little
  trickier
• They are visibly not a continuum, rather lots of
  tiny grains (think rigid bodies) in frictional
  contact
• But, if the of grains is large, in most
  situations can be approximated as a continuum
• Flow laws come out of frictional contact laws

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Mohr-Coulomb

• Basic continuum model Mohr-Coulomb (continuum
  generalization of Coulomb friction)
• Sand remains rigid (or slightly elastic) if the
  pressure (normal force) is larger than some
  constant times the shear stress (tangential
  force)
• If it flows, it has a viscous term proportional
  to pressure (not rate of flow!)

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Sand vs. Water

• Hydrostatic (not moving) water pressure increases
  linearly with depth
• the bottom supports weight of all the water above
  it
• Sand pressure reaches a maximum friction
  transfers load to walls
• the bottom only supports some of the weight above
  it, and the walls the rest
• See this effect in silo failures and in
  hourglasses

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Approximation!

• That said, for many piling-up cases, the water
  pressure is a good approximation to sand pressure
• Idea compute incompressible flow as if for
  water, then add friction effects in at the end
• Estimate tangential force needed to stop flow in
  grid cell
• If pressure is large compared to that, mark cell
  as rigid
• Rigidify connected groups of rigid cells (find
  translational and angular velocity)
• Apply friction-like viscosity elsewhere

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Movies

• Sand models collapsing

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Thank You!

• Web site http//www.cs.ubc.ca/rbridson/fluidsimul
  ation will be updated with notes and code