Viscoelasticity

2. Viscoelasticity

3. 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)

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 [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)

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/fluidsimulationwill be updated with notes and code