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
Made with FlippingBook - Online catalogs