Viscoelasticity

Viscoelasticity

• While water and air are Newtonian, lots of other common stuff isn’t:

– 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)

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

Regular Viscoelasticity

• See [Goktekin et al.’04] and [Irving’06]

• 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)

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

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!)

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

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

Movies

• Sand models collapsing

Thank You!

• Web site http://www.cs.ubc.ca/~rbridson/fluidsimulation will be updated with notes and code