Example 6 : Particle Packing in Ball (Three dimensional)
A three-dimensional discrete element method simulation of particle packing in a ball (sphere) geometry is performed in this example.
Total simulation time is equal to 1 s, while time-step, log frequency and output frequency are set equal to 0.000001, 1000 and 1000, respectively:
# --------------------------------------------------
# Simulation and IO Control
#---------------------------------------------------
subsection simulation control
set time step = 1e-6
set time end = 1
set log frequency = 10000
set output frequency = 10000
end
In the model parameters section, particle-particle and particle-wall broad and fine search frequencies are defined. The contact detection method is dynamic. We also define the particle contact search size (neighborhood threshold), contact forces and integration methods:
# --------------------------------------------------
# Model parameters
#---------------------------------------------------
subsection model parameters
set contact detection method = dynamic
set dynamic contact search size coefficient = 0.5
set neighborhood threshold = 1.4
set particle particle contact force method = pp_nonlinear
set particle wall contact force method = pw_nonlinear
set integration method = velocity_verlet
end
In the physical properties section, the physical properties of particles and walls, including diameter and density of particles, Young's modulus, Poisson's ratios, restitution coefficients, friction and rolling frictions of particle and wall are chosen. The gravitational acceleration is also set in this section. It should be mentioned that in this example the gravitational acceleration is a three-dimensional vector, despite the two-dimensional example (Example 5).
#---------------------------------------------------
# Physical Properties
#---------------------------------------------------
subsection physical properties
set gx = 0.0
set gy = 0.0
set gz = -9.81
set number of particle types = 1
subsection particle type 0
set size distribution type = uniform
set diameter = 0.005
set number = 5000
set density particles = 2000
set young modulus particles = 10000000
set poisson ratio particles = 0.3
set restitution coefficient particles = 0.75
set friction coefficient particles = 0.2
set rolling friction particles = 0.1
end
set young modulus wall = 10000000
set poisson ratio wall = 0.3
set restitution coefficient wall = 0.75
set friction coefficient wall = 0.2
set rolling friction wall = 0.1
end
Next, we define the insertion properties, which are insertion method, inserted number of particles at each insertion step, insertion frequency, insertion domain and other information regarding the initial positions of particles inside the insertion domain:
#---------------------------------------------------
# Insertion Info
#---------------------------------------------------
subsection insertion info
set insertion method = non_uniform
set inserted number of particles at each time step = 1000
set insertion frequency = 150000
set insertion box minimum x = -0.05
set insertion box minimum y = -0.05
set insertion box minimum z = -0.03
set insertion box maximum x = 0.05
set insertion box maximum y = 0.05
set insertion box maximum z = 0.07
set insertion distance threshold = 2
set insertion random number range = 0.75
set insertion random number seed = 19
end
Finally, the triangulation information, which defines the geometry of the simulated system are defined. The radius of the packing domain sphere in this case is equal to 0.1 m and the center of the sphere is located at (0, 0, 0):
#---------------------------------------------------
# Mesh
#---------------------------------------------------
subsection mesh
set type = dealii
set grid type = hyper_ball
set grid arguments = 0.0, 0.0, 0.0 : 0.1 : false
set initial refinement = 3
end
This example should be solved using dem_3d solver. The particle are packed inside the defined sphere:
