Issue 47

E. Mele et alii, Frattura ed Integrità Strutturale, 47 (2019) 186-208; DOI: 10.3221/IGF-ESIS.47.15

s   

1 2 -1

1

  

  s 

(5)

P



s 

s    -1,

0

1



Therefore the perturbed coordinates (x 1 s , x 2 s ) are defined by using the following equations:

s 1





s 1

0 s x x α d Cos      s x x α d Sin      s   s s 2 2 0 s

(6) (7)

where α  [0,1] defines the irregularity degree of the Voronoi grid, namely α = 0 corresponds to the regular hexagonal grid, while α = 1 corresponds to Voronoi grid with maximum degree of irregularity. The last step is to apply the Voronoi tessellation rule to the arrays of points modified through the Eqns. (6) and (7), in order to obtain patterns with irregularity governed by the value of the parameter α. The fundamental role played by α is clearly shown in Fig. 5, which provides three specimens with the same overall dimensions and number of seeds (i.e. of initial hexagons), but with different degree of irregularity, i.e. different values of α adopted in the generation process.

Figure 4 : Geometric perturbation of the coordinates of regular array of seeds.

For α = 0, a regular honeycomb structure is generated; increasing α, the irregularity of the pattern increases, and for α = 1, a geometry with the maximum irregularity degree is obtained. Of course, for each values of α (i.e. for each level of irregularity), infinite geometric configurations can be generated varying the random parameters  s and ϑ s .

Figure 5 : Effect of the irregularity parameter α: α = 0; α = 0.5; α = 1.

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