% Strain
S
tr
ess(
M
P
a)
n1_K11
n2_K24
n3_K52
n4_K110
n4_K120
n5_K220
n6_K466
Figure 3.2. Stress versus strain for different core strand properties (n, K).
0
5
10
15
20
25
30
35
0
0.1
0.2
0.3
0.4
0.5
0.6
Strain
S
tr
ess (
M
P
a)
Elastic
Buckling
Densification
44
3.3.2 Hill Plasticity Material (Model)
All of the previous material studies of wood composites (such as on OSB, PSL, I-
beam) have used Finite Element Analysis (FEA). Bai et al. (1999) modeled the behavior
of Moso bamboo-reinforced OSB composite beams. In the model, OSB was assumed to
be an elastic-orthotropic material. The study focused on flexural behavior as related to the
combined effects of bamboo, OSB, and the adhesive layers. Moris et al (1995) developed
a two dimensional FEA model to predict the shear strength of OSB webbed I-beams with
and without a circular opening. OSB was treated as a linear elastic orthotropic material
and a Tsai- Hill failure criterion was applied in tension while the compressive strength
and yield of OSB were neglected. Saliklis and Mussen (2000) investigated the buckling
behavior of OSB panels using the FE method. OSB was modeled as an elastic orthotropic
material in an eigenvalue buckling analysis, and in a nonlinear buckling analysis it was
modeled as a bilinear elasto-plastic material with the second portion of the constitutive
curve having either a small or a zero modulus. The yield stress was taken to be 95% of
the ultimate stress.
Guan et al (2005) used an elastic-plastic stress-strain relationship to
develop an FE model to simulate OSB in compression and in tension. A parabola-like
curve between initial yield and the ultimate stress, which represents the nonlinear stress-
strain relationship of OSB was developed.
In this study plasticity of the strands was modeled using
J
2
plasticity theory (Simo
and Hughes 1997), an anisotropic Hill yielding criterion (Hill 1948), and the power-law
work hardening term (Simo and Hughes 1997) from the previous section. The plain strain
plastic potential for this material response was
)
1
(
2
2
2
n
p
Y
xy
xy
y
x
z
x
z
y
Y
z
z
Y
x
y
Y
x
x
K
H
G
F
f
ε
τ
τ
σ
σ
σ
σ
σ
σ
σ
σ
σ
σ
σ
σ
+
−
+
−
−
−
+
+
=
(3.2)
where
i
σ
and
xy
τ
are the normal and shear stresses in the material’s axis system,
Y
i
σ
is the
tensile yield stress in material direction
i
, and
Y
xy
τ
is the shear yield stress in the
material’s x-y plane,
45
( ) ( ) ( )
2
2
2
1
1
1
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