Biomedical Engineering Reference
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is only necessary that
be positive, in which case
b
can be set to zero. Coupling
between the damage modes can be included. For example (6.59) can be modified to
the rate of enzymatic damage is depemdent on the strain state of the tissue.
η
Effect of combined damage modes
Following Miehe 1995 [78], when more than one damage mode are involved, we can
define the damage parameter as the sum of the damage parameters for the various
modes so that the reduction factor given in (6.41) becomes in [78],
(
1
−
d
)=(
1
−
d
1
−
d
2
−
d
3
)
(6.60)
with (6.51). In this case, we must impose the additional restriction that condition that
d
1
+
1. Namely, the combined damage must not exceed complete damage
for the material. An alternative choice is to consider a multiplicative combination of
these two modes,
d
2
+
d
3
≤
(
1
−
d
)=(
1
−
d
1
)(
1
−
d
2
)(
1
−
d
3
)
.
(6.61)
In this case, there is no additional restriction beyond (6.51).
The damage metrics
α
1
(
t
)
,
α
2
(
t
)
are clearly invariant to superposed rigid body
motions. The form of
3
defined in (6.57) is purposely left quite general, but will
similarly be an invariant quantity.
α
6.4.3 Damage assessment using the UA-MPM device
Two human basilar arteries were obtained from cadaver circles of Willis, cut into
segments, and tested in the UA-MPM device, using the previously described proto-
col [49], as mentioned in Sect. 6.3.5. Uniaxial damage experiments were performed
with the UA-MPM system on artery segments until total large scale mechanical tears
of the IEL were confirmed. We modelled the undamaged arterial wall as a single
layer multi-mechanism material, and discontinuous damage was modelled as de-
scribed in Sect. 6.4. Thus, the strain energy function was modified to give
W
=(
1
−
d
1
(
α
))
W
iso
+
W
aniso
(6.62)
with
W
iso
given as in Eq. 6.40. The scalar-valued isotropic damage parameter for
discontinuous damage
d
1
was given by (6.52) , with the damage accumulation metric
α
1
(
given by Eq. (6.53). We assumed the anisotropic response was dominated by
circumferentially-oriented medial collagen fibres.
W
aniso
was defined as in (6.19)
with
N
t
)
1. Collagen recruitment occurred when the circumferential stretch ratio
exceeded the activation stretch,
=
λ
a
.
Data were fit to the discontinuous damage model via nonlinear regression to
obtain material and damage parameters (Fig. 6.11). At high strain, the intima re-
gion split perpendicular to the circumferential loading direction and peeled away
from the media, as observed from visual inspection and images taken from a CCD
camera (Fig. 6.12). Multi-photon images revealed a cat's eye-shaped longitudinal
tear in the internal elastic lamina, which pulled back under strain to reveal mostly
