psl_purdue_dem_lecture02_hardparticlecontactmodel.pdf

C. Wassgren, Purdue University 1 DEM Modeling: Lecture 02 Introduction to the Hard-Particle Algorithm Collision Model C. Wassgren, Purdue University 2 Introduction ? Hard particle simulations are deterministic - given the same initial conditions the final results will be the same – the state of every particle in the system and all particle interactions are determined using physical laws ? The term “hard-particle” refers to the fact that particles are considered to be perfectly rigid – ? particles do not deform during a collision – ? collisions occur instantaneously – ? only binary (two particle) collisions occur ? Used most often for modeling dilute, energetic granular flows C. Wassgren, Purdue University 3 x ≡ position ω ≡ angular velocity m ≡ mass r ≡ radius I ≡ moment of inertia J ≡ impulse of momentum acting on particle 1 due to collision with particle 2 ≡ unit vector pointing from the center of particle 1 to the center of particle 2 y x z x1 x2 m2, r2, I2m1, r1, I1 ω1 ω2 J n? n? Collision Dynamics collisiont dt= ∫J F Assuming spheres ? I = 2/5mr2 C. Wassgren, Purdue University 4 Collision Dynamics… ? Unit normal vector for the contact (assuming spheres) ? Velocity of particle 2 relative to particle 1 at the point of contact 2 1 2 1 ? ? = ? x x n x x ( ) ( ) ( ) 1, 1 1 1 2, 2 2 2 2, 1, 2 1 2 2 1 1 ? ? ? ? C C C C C r r r r = + × = + × ? ? = ? = ? ? × + × x x ω n x x ω n x x x x x ω n ω n ? ? ? ? ? ? ? ? ? C. Wassgren, Purdue University 5 Collision Dynamics… ? Unit tangential vector for the contact – perpendicular to unit normal and points in the direction of the relative contact velocity just prior to the collision ? Normal and tangential components of the impact velocity ( ) ( )? ? ? ?C C C? ? ?? = ? ? + ? ?x x n n x s s? ? ? ? ? C C n s = ? ? = ? ? x n x s ? ? ? ? ( ) ( ) ? ? ? ? ? C C C C ? ? ? ? ? ? ? ? = ? ? ? ? x x n n s x x n n ? ? ? ? C. Wassgren, Purdue University 6 Collision Dynamics… ? Conservation of linear momentum for each particle ? Co