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Bog'liq
Edward Le PhD Dissertation

1/(1-C)
M
O
E
(M
P
a
)
40%VTC, 1/D
t
=0
40%VTC, 1/D
t
=0.05
HROM


75 
3.8 Summary and Conclusions 
This study has demonstrated that MPM can handle large-scale, morphology-based 
models of real wood-based composites including glue-line effects, strand undulation and 
compaction effects. It is easy to generate a wood-strand composite structure based on 
strand length, strand gap, and strand thickness. Once the random structure of a wood-
strand composite is completed, it can then be compressed. The structure can also include 
elastic-plastic and work hardening properties during compaction and yielding. Once the 
structure is compressed, tension load can be applied to find MOE. 
The mechanical properties increased as compaction levels increased. Furthermore, 
the numerical calculation can also test mechanical properties as a function of interfacial 
properties. A glue-line interfacial property affects the mechanical properties of the entire 
composite. As the interfacial properties increased (from discrete droplets [1%] to 
continuous bond line [100%]), the mechanical properties of strand-based composites 
increased. There are higher mechanical properties when using VTC strands in the surface 
layers with 20% and 40% weight fractions. There is more increase in mechanical 
properties when using VTC strands in all the surface layers. In order to compare the 
stiffness values to the experiment data, more work is needed to determine the amount of 
compaction in the OSB panels. 


76 
Appendices 
Appendix 3.1: Generalize interpolation material point method (GIMP) derivation
In solid mechanics, the deformation of a continuous solid body under load is 
governed by conservation of mass and momentum. The virtual work or power can be 
formulated as a general equation of momentum as: 
dV
u
dV
u
a
u
F
dS
u
T
dV
u
b
V
V
P
P
S
V
T






δ
σ
δ
ρ
δ
δ
δ
ρ

+

=

+

+






:
(3.10) 
where 
σ, ε and u are stress, strain and displacement. 
b

and 
P
F

are specific body force 
(such as gravity) or point loads. 
T

is surface traction
a

is acceleration, 
u

δ
is virtual 
displacement and ρ is density. In MPM, this equation
is solved in a Lagrangian frame on 
a grid.
A Lagrangian formulation means that the acceleration does not contain the 
convection term which can cause significant numerical errors in purely Eulerian 
approaches. During this Lagrangian phase of the calculation, each element is assumed to 
deform in the flow of the material so that points in the interior of the element move in 
proportion to the motion of the nodes. That is, given the velocity at the nodes determined 
from Eq. (3.10), the element shapes are updated by moving them in this single-valued, 
continuous velocity field. Similarly, the velocity and position of a material point is 
updated by mapping the nodal accelerations and velocities to the material point positions.
In this method, the mesh does not conform to the boundary of the object being 
modeled. Instead, a computational domain is constructed in a convenient manner to cover 
the potential domain for the boundary-value problem being solved. Then the object is 
defined by a collection of material points. As material points move, they transport 
material properties assigned to them without error. In MPM, the material points carry 
enough information to reconstruct the solution; therefore one can choose whether to 
continue the calculation in the Lagrangian frame or map information from the material 
points to another grid. This feature avoids mesh tangling which can occur in a purely 
Lagrangian calculations under large strains, and allows one to choose the grid for 


77 
computational convenience. In practice, the deformed grid is discarded after each time 
step and the next time step begins with a new, regular mesh.
In MPM the body is divided into particles of mass 

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