Computational modeling of soft tissues and ligaments 151
s
ss
s
s
s
s
s
*
*
s
s
s
*
s
s
s
*
x
s
s
s
s
(
(
)
)
(
)
∫
d
τ
τ
0
∫∫
and
e
ee
ee
e
ee
*
*
e
ee
*
e
ee
*
x
e
e
ee
(
(
)
)
(
)
∫
d
τ
τ
0
∫
∫
are the local stress and strain
second order tensors, respectively; and the fourth-order tensor C
*
is de ned
as:
C
C
C
**
**
*
**
x
xx
x
(
)
=
(
)
∈
∈
⎧
⎨
⎧
⎧
⎩
⎨
⎨
ff
,
xx
,
(
)
∈
MM
,
x
∈
ΔΩ
ΔΩ
[5.19]
Consistently with a homogeneous strain approach, for an assigned incre-
ment
e
e
ee
x
(
)
d
τ
d
and depending on the de nition of
ΔΣ
T
, the boundary displace-
ment
u
*
has to be chosen such that
e
ee
ee
e
ee
av
e
e
*
e
ee
, where
g
av
*
denotes the mean
value of the microscale eld
g
**
x
(
)
over
ΔΩ
T
. In this way, computing the
macroscale stress increment ...
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