Modeling of Granular Materials Abhinav Golas COMP 768 - Physically Based Simulation April 23, 2009 1 Motivation  Movies, games Spiderman 3 The Mummy  Engineering design – grain silos  Avalanches, Landslides www.stheoutlawtorn.com April 23, 2009 2 Overview  What are Granular Materials?  Simulation  Rendering April 23, 2009 3 Overview  What are Granular Materials?  Simulation  Rendering April 23, 2009 4 What are Granular Materials?  A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (Wikipedia)  Size variation from 1μm to icebergs  Food grains, sand, coal etc.  Powders – can be suspended in gas April 23, 2009 5 What are Granular materials?  Can exist similar to various forms of matter Gas/Liquid – powders can be carried by velocity fields  Sandstorms  Liquid/Solid – similar to liquids embedded with  multiple solid objects Avalanches, landslides  Hourglass   Similar to viscous liquids April 23, 2009 6 Why the separate classification?  Behavior not consistent with any one state of matter Can sustain small shear stresses – stable piles 1. Hydrostatic pressure achieves a maximum  Particle interactions lose energy 2. Collisions approach inelastic  Infinite collisions in finite time – inelastic collapse  Inhomogeneous and anisotropic 3. Particle shape and size inhomogeneous  Granular solids, liquids, and gases – Jaeger et al. April 23, 2009 7 Understanding the behavior - Stress y F z  Stress  A y     xx xy xz   z Shear       yx yy yz       zx zy zz Normal  At equilibrium – matrix is symmetric – 6 degrees of freedom  Pressure for fluids – tr(σ)/ 3 April 23, 2009 8 Stress  Different matrix for different basis – need invariants Pressure! – I  0 Deviatoric invariants – Invariants based on   I   0  J ,J 1 2  Eigen values? – called principle stresses April 23, 2009 9 Understanding the behavior  Why can sand sustain shear stress? Friction between particles   When does it yield? – yield surface/condition April 23, 2009 10