## Aggregate Packing Generator with Fibers

version 1.0.3 (10.7 KB) by
Aggregate packing generator with fibers used for the simulation of aggregate and fibers in composites

Updated 7 Jan 2021

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

1-function Classes=Particles_Generation(x,y,z,Classes_diameters,Alpha,m,Particle_ratio)
Generates aggregates according to Fuller's curve.
2-function Plot_Sieve(Classes,x,y,z,Classes_diameters,Alpha,Particle_ratio)
Plots generated sieve curve.
3-function Ellipsoids=Particles_Distribution(Classes,x,y,z,er)
Generates aggregate with ellipsoids shapes
4-function Plot_Ellipsoids(Ellipsoids,x,y,z)
Plots ellipsoids
5-function Ellipses=Ellipsoids_to_Ellipses(Ellipsoids,dist,r_min)
Converts ellipsoids to ellipses. used for 2D analysis
6-function Plot_Ellipses(Ellipses,x,z)
Plots ellipses
7-function [Nodes_Fibers, Fibers]=Generate_Fiber(x,y,z,L,N,Orientation,Ndiv,Ellipsoids);
Generate fibers
8-function Plot_Fiber(x,y,z,Nodes_Fibers,Fibers)
Plots fibers
9-function Plot_Ellipsoids_Fiber(Ellipsoids,x,y,z,Nodes_Fibers,Fibers)
Plot ellipsoids with fibers
where the variables defined as:

input:
x,y,z: as vectors defining the specimen dimension. x and z are vectors defining a polygon section in xz plane and y=[ymin ymax] is boundaries of the extrusion of the polygon
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.
L: Length of fibers
N: Number of fibers
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

Output:
Classes: A variable containing generated particles and not yet packed into specimen
Ellipsoids: (N*9) array. each column represent:
(:,1): radius of ellipsoids at direction 1
(:,2): radius of ellipsoids at direction 2
(:,3): radius of ellipsoids at direction 3
(:,4): x-cooridante of centroid
(:,5): y-coordinate of centroid
(:,6): z-coordinate of centroid
(:,7): Inclination angle 1
(:,8): Inclination angle 2
(:,9): Inclination angle 3

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

Nodes_Fibers: ((Ndiv+1)*N,3) matrix of fibers nodes coordinates.

Fibers: (N,2) matrix of the two nodes indices connecting each fiber segment.

references
 Unger, Jörg F., and Stefan Eckardt. "Multiscale modeling of concrete." Archives of Computational Methods in Engineering18.3 (2011): 341.
 Fang, Qin, and Jinhua Zhang. "Three-dimensional modelling of steel fiber reinforced concrete material under intense dynamic loading." Construction and Building Materials 44 (2013): 118-132.

### Cite As

Ayad Al-Rumaithi (2022). Aggregate Packing Generator with Fibers (https://www.mathworks.com/matlabcentral/fileexchange/85248-aggregate-packing-generator-with-fibers), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2017b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux