Percolation of Fibers with Aggregate

Determines the percolation of fibers in a box (cuboid) containing aggregate

This example file (Example.m) determines the percolation of fibers in a box (cuboid) containing aggregate. The input values are:

Vf: Volume fraction of fibers in the bigger box

Bx: Side length of the box in x-direction

By: Side length of the box in y-direction

Bz: Side length of the box in z-direction

L: Length of fibers

d: Diameter of fibers

Classes_diameters: Particles classes diameters vector (descendingly)

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

m: Particles shape distribution factor. m=1 for spheres and m>>1 for elongated ellipsoid shapes.

Particle_ratio: Particles ratio of the total volume 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].

dist: Cutting distance for converting ellipsoids to ellipses.

r_min: Minimum ellipse radius involved when ellipsoids are converted to ellipses.

Orientation: can be either:-

-For aligned fibers Orientation=[l m n] where l,m, and n are the direction cosines of the fibers orientation in x,y, and z directions, respectively.

- For random fibers Orientation=[] (empty)

Ndiv: Number of fiber mesh divisions

The fibers are generated in a bigger box of size (Bx+4*L, By+4*L, Bz+4*L), then cropped into the original (smaller) dimensions (Bx, By, Bz). The reason behind that is to ensure that fibers are uniformly distributed across the domain. The volume fraction of fibers in the smaller box is slightly bigger than Vf. After that, percolation is determined in z-direction from Z=0 to Z=Bz. The criteria for percolation is that the distance between fibers is d, and the distance between fibers and the planes (Z=0, Z=Bz) is d/2. If there is percolation then the value of Percolation variable is 1, otherwise it is zero.

A number of figures are plotted including: 1-fibers in the bigger box, 2-cropped fibers in the smaller box, and 3-the fibers with percolation in the smaller box.

The value of Vf can be increased or decreased, and the percolation will change accordingly.