Multiscale Elastic Models of Collagen Bio-structures: From Cross-Linked Molecules to Soft Tissues - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 77

Fig. 2 Typical stress/strain
curve for unidirectional
regular soft collagenous
tissues such as tendons and
ligaments
walls) directional. A multi-directional tissue is intended to be made up of a
number of stacked thin layers, each of them with a regular uni-directional fiber
arrangement.
As confirmed by well-established studies [ 2 ], constitutive response of soft
collagenous tissues depends primarily on the mechanical behavior of collagen fibers
and molecules. For instance, in the case of a uni-directional tissue subjected to a
uni-axial tensile test along the fiber direction, a progressive fiber straightening and
the disappearance of nanoscale kinks within molecules are experienced, resulting in
an increase of the overall tissue stiffness. Accordingly, the stress/strain curves are
typically J-shaped and can be subdivided into three main regions (Fig. 2 ):
• Toe region: the region of small tissue strains (up to 2 %), related to the removal
of the microscopic crimp in collagen fibers.
• Heel region: at strains 2-4 %, characterized by a significant stiffening response
due to the entropic straightening of nanoscale molecular kinks [ 2 , 9 ].
• Linear region: when the tissue is stretched beyond the heel region, most kinks
are straightened and no further extension is possible by entropic mechanisms.
Therefore, the mechanical response is primarily affected by the stretching of the
collagen triple-helices and by molecular rearrangement (collagen sliding) [ 26 ].
It should be pointed out that, despite of similar features at the nanoscale,
different types of collagenous tissues can be characterized by significantly different
mechanical responses, mainly depending on histological composition and orga-
nization at lower scales. In the following, two different regular soft collagenous
tissues, with different complexity in terms of collagen arrangement, geometry and
loading conditions, will be addressed: tendons and the tunica media of the aortic
walls.
2.2.1 Tendons
Tendons are regular dense connective tissues, transmitting muscular forces and
playing a crucial role in the functioning of joints and musculo-skeletal system. The
mean axis of collagen fibers in tendons is mainly aligned along the loading