Aggregate 2D Packing Generator

Aggregate 2D packing generator used for the simulation of aggregate in composites

Aggregate 2D packing generator used for the simulation of aggregate in composites. It can be used especially for meso-scale analysis of concrete and asphalt composites .Example files are provided for the simulation of aggregate in notched beam section "Example_Beam.m" and cylinder section "Example_Cylinder.m"

1-function Classes=Particles_Generation(x,y,Classes_diameters,Alpha,m,Particle_ratio)

Generates aggregates according to Fuller's curve.

2-Plot_Sieve(Classes,x,y,Classes_diameters,Alpha,Particle_ratio)

Plots generated sieve curve.

3-Ellipses=Particles_Distribution(Classes,x,y,er)

Generates aggregate with ellipses shapes

4-function Plot_Ellipses(Ellipses,x,y)

Plots ellipses

where the variables defined as:

input:

x,y: as vectors defining the specimen dimension. x and y are vectors defining a polygon section.

Classes_diameters: Particles classes diameters vector (descendingly)

Alpha: Fuller's curve exponent [0.45-0.5].

m: Particles shape distribution factor. m=1 for circles and m>>1 for elongated ellipses shapes.

Particle_ratio: Particles ratio of the total area including the smaller particles not simulated in the analysis. ranges [0.6-0.9] for portland cement concrete and about 0.9 for asphalt concrete.

er: Spacing factor between particles to avoid contact [0.05-0.1].

Output:

Classes: A variable containing generated particles and not yet packed into specimen

Ellipses: (N*5) array. each column represent:

(:,1): radius of ellipses at direction 1

(:,2): radius of ellipses at direction 2

(:,3): x-cooridante of centroid

(:,4): y-coordinate of centroid

(:,5): Inclination angle

Important Notes:

1-the function overlap.m should detect intersection between two ellipses but it does not work correctly. The ellipses are still seperated using the bounding box overlap check.

2-particle_diameter.m equation is derived based on ellipsoids not ellipses in Unger paper[1].

references

[1] Unger, Jörg F., and Stefan Eckardt. "Multiscale modeling of concrete." Archives of Computational Methods in Engineering18.3 (2011): 341.

[2] Choi, Y-K., et al. "Continuous collision detection for two moving elliptic disks." IEEE Transactions on Robotics 22.2 (2006): 213-224.