Biomedical Engineering Reference
In-Depth Information
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Fig. 8.9
Collagen fibril micromechanical model [
243
]. A model put fourth for collagen fibers
consisted of fibrils of a finite length and with tapered tips connected via proteoglycan matrix
material (
Left
). A quarter symmetric micromechanical model was defined (
Right
) and subjected to
simulated loading. Figure adapted from [
243
]
interfibril matrix [
243
,
244
]. In these studies, a 2D plane strain model was used
to examine force transfer between adjacent collagen fibrils via an interfiber matrix
[
243
]. A unit cell was created that consisted of a discretized fibril embedded within
a matrix material (Fig.
8.9
). The fibrils were given cylindrical or tapered endpoints
[
244
]. The unit cell was subjected to homogenous boundary conditions, in which
a displacement was applied to the sides of the model. The aspect ratio of the fiber
and applied load were varied parametrically and their influence on the fibril stress,
interfiber force transfer and strain was examined. Simulations revealed that fiber
strain displayed a dependency on the end shape of the fibril, on the fibril aspect ratio
and the ratio of the fibril stiffness to the matrix stiffness. The effect of tapered fibril
ends was to decrease stress within fibers. The effect of increasing the stiffness of
the inter fibril matrix was to increase load sharing between fibril and the matrix,
which yielded decreased fibril strains. By utilizing a unit cell approach, this study
was able to examine the influence of structure-function relationships that would be
difficult if not impossible to investigate using experimental or analytical approaches.
Within these studies, the concept of an interfiber matrix material was utilized. The
matrix material is thought to consist of PGs, elastin and other ECM proteins that may
mechanically couple collagen. Such a concept has been used in numerous studies
(e.g., [
132
,
133
,
238
,
245
,
246
]) and is used to describe the substance that mechan-
ically couples collagen fibrils and fibers within tendon and ligament.
One area that shows great promise in the field of multiscale modeling is the study
of stress and strain localization as it pertains to damage initiation. Although no stud-
ies have yet utilized micromechanical models to study damage initiation in tendon,
they have been utilized in studying microscale strain patterns in the myotendinous
junction (MTJ), which displays similarities to tendon and ligament tissue. In one
such study, a 2D micromechanical model was used to explore microscale strain dis-
tributions within the MTJ, a common location for musculoskeletal injuries [
224
].
At the MTJ, muscle fibers taper as they insert into the tendon via the endomysium,
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