Issue 49

A. Bendada et alii, Frattura ed Integrità Strutturale, 49 (2019) 655-665; DOI: 10.3221/IGF-ESIS.49.59

F is the applied force on the RVE when the displacement i U 

where i

is imposed, S i

is the perpendicular surface to the

displacement. Poisson’s ratios are determined by the following equation:

j 

ij 

 

j 

, , , i j x y z 

with i

(2)

i 

 , j

 are given by the following equations:

where the deformations i

j U l

i U l

j

i

 

 

and

(3)

i

j

with , l represents the length, thickness and width of the RVE. The boundary conditions applied in each case for identifying the Young’s moduli are given in Tab. 3, Tab. 4 presents the deformation of the RVE in each extension numerical simulation. i j

x direction

y direction

z direction

0 y 

0 z 

0 x 

0.0 x U mm  x U mm  1.0 0.0 y U mm  z U mm  0.0

0.0 y U mm  y U mm  1.0 0.0 x U mm  z U mm  0.0

0.0 z U mm  y U mm  0.1 0.0 x U mm  y U mm  0.0

x L 

y L 

z L 

y

z

x

y L 

/ 2 y

x L 

x L 

/ 2 x

/ 2 x / 2 y

z L 

z L 

y L 

/ 2 z

/ 2 z

Table 3 : Extension boundary conditions.

x direction

y direction

z direction

(a)

(b)

(c)

Table 4 : RVE 0

undeformed shape, RVE 1

deformed shape, in each case of extension simulation.

G , xz

G , yz

G are determined by the equation:

Shear moduli xy

i i I F G

S l l  

j k   , ik i

, i

(4)

k

ij

ik i S U 

U  along the directions x ,y, z . The boundary

i F is the resulting shear forces in direction i by applying the displacement i

conditions and deformation shape are given in Tab. 5-6.

658

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