  Collagen fibrils are the most important structural component of tendons.
Their crimped structure and parallel arrangement within the tendon lead to a
distinctive non-linear stress-strain curve when a tendon is stretched.
Microstructural models can be used to relate microscale collagen fibril
mechanics to macroscale tendon mechanics, allowing us to identify the
mechanisms behind each feature present in the stress-strain curve. Most models
in the literature focus on the elastic behaviour of the tendon, and there are
few which model beyond the elastic limit without introducing phenomenological
parameters. We develop a model, built upon a collagen recruitment approach,
that only contains microstructural parameters. We split the stress in the
fibrils into elastic and plastic parts, and assume that the fibril yield
stretch and rupture stretch are each described by a distribution function,
rather than being single-valued. By changing the shapes of the distributions
and their regions of overlap, we can produce macroscale tendon stress-strain
curves that generate the full range of features observed experimentally,
including those that could not be explained using existing models. These
features include second linear regions occurring after the tendon has yielded,
and step-like failure behaviour present after the stress has peaked. When we
compare with an existing model, we find that our model reduces the average root
mean squared error from 4.15MPa to 1.61MPa, and the resulting parameter values
are closer to those found experimentally. Since our model contains only
parameters that have a direct physical interpretation, it can be used to
predict how processes such as ageing, disease, and injury affect the mechanical
behaviour of tendons, provided we can quantify the effects of these processes
on the microstructure.
