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Viscoelasticity

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Granular materials like sand are a little trickier ... Sand remains rigid (or slightly elastic) if the pressure (normal force) is ... – PowerPoint PPT presentation

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Title: Viscoelasticity


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(No Transcript)
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Viscoelasticity
3
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)

4
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

5
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)

6
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

7
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!)

8
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

9
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

10
Movies
  • Sand models collapsing

11
Thank You!
  • Web site http//www.cs.ubc.ca/rbridson/fluidsimul
    ation will be updated with notes and code
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