PSI - Issue 32

Nataliya Elenskaya et al. / Procedia Structural Integrity 32 (2021) 253–260 N. Elenskaya, M. Tashkinov / Structural Integrity Procedia 00 (2019) 000 – 000

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Graded structures can be created based on these unit cells using density gradient, heterostructure gradient and cell-size gradient. The table 1 shows the expressions that were offered for the porosity gradient structures.

Table 1. Expressions for typical porosity gradient structures

TPMS unit cell

Mathematical expressions

01 , G G G R    

1 1 , G R k y R  

1 0.03, k 

1 0.4. R  (Liu et al., 2018)

1.5,      

with



 , , ,

02 G G x y z   

0.048 1.123 0.078 , y y

1.123 0.132 , y     

   

(Liu et al., 2018)

with









    C cos 2 cos 2 cos 2 cos 2 cos 2 cos 2 , x z z y z x                

03 G G x y z    , ,



0

0.048 1.123 0.078 , y y

0.08.

1.123 0.132 , y     

0 C 

   

(Liu et al., 2018)

with





04 G G x y z C     , ,

,

1

1

1

 

  

1.33 1 

0.87

,

  

  





with

G (Gyroid) surface









0.5 7.5 x

0.5 0.75 x

 

 

1

1

e

e





0.85.

C  

(Zhang et al., 2020)

1

    G x     05 G G





   G





  x   G



, , x y z C

1   

, , x y z C 

,

2

3

1

1

1 ,

 

  

  x

0.85,

1.33 1 

0.87

,

C  

  

  









with

2









G

  0.5 12.05 y

0.5 12.05 y

0.5 12.05 y

 

 

 

1

1

1

e

e

e







0.3,

C  

(Zhang et al., 2020) I WP x y z R y       , ,

3

,







01

I WP 

I WP 

 

1,      

0.105 . y

I WP R y 

 

with



 , , ,

I WP x y z  





02

I WP 

1.         , , I WP x y z C   

with

,





03

4

I WP 

1.89.

1,      

C  

with

4

  y    3





  y    3







 , , ,

, , x y z C

1   

x y z





04

5

I WP 

I WP 

I WP 

   0.5 12.05 6 1 y x   

  , x y

2.4.

1,      

,

C  

 



I-WP surface

with

5

I WP

1

e







, , I WP x y z C   

,





05

6

I WP 

1

1

 

  

1.33 1 

0.87

,

  

  





with









0.5 12.05 y

0.5 12.05 y

 

 

1

1

e

e





0.85.

C  

(Zhang et al., 2020)

6

Here , , x y z are coordinates. The functions

02 I WP   and

03 I WP   specify non-gradient models and are presented for

comparison with the gradient model, which is defined by the function 01 . I WP   Resulting open-cell microstructure models are presented on Fig. 2-3. The cell-size was equal for all structures with dimensions 12 24 12   mm,       0,12 , 0.1, 24.1 , 0,12 x y z    .