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associated with a Voronoi polyhedron, as discussed by Cambou
et al
. [CAM 00].
N
is the total number of contact orientations. The variables
j
α
δ
and
k
α
l
are defined as
δ
and
l
, respectively, for all contacts belonging to the
the averaged values of
j
th
α
orientation.
7.2.3.
Model parameters
We can summarize the material parameters as:
3
- normalized contact number per unit volume:
Nl V
;
/
- mean particle size,
d
;
- interparticle elastic constants:
k
n0
,
k
t0
and
n
;
- interparticle friction angle: φ
μ
and
m
;
- interparticle hardening rule:
k
p0
and φ
0
;
- critical state for the packing: λ and Γ or
e
ref
and
p
ref
.
We obtain two classes as discussed in the introduction:
- those that are independent of the arrangement and are connected to the contact
law:
k
n0
,
k
t0
,
n
, φ
μ
,
m k
p0
and φ
0
;
- those that describe the geometry of the arrangement and its mechanical state:
N
=
3
αα
Nl V
,
d,
λ and Γ or
e
ref
and
p
ref
, and the fabric tensor
/
A
l l
in the
ik
i k
α=
1
case of an anisotropic assembly. The latter case will not be discussed in this study.
Standard values for
k
p0
and φ
0
are the following:
k
p0
=
k
n
and φ
0
= φ
μ
and a typical
ratio
0
kk
= 0.5 can be generally assumed. Therefore, only six parameters have
to be derived from experimental results and they can all be determined from the
experimental data obtained from the material studied. The following section shows
some examples on Hostun sand.
n
0
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