  A new strain energy function for the hyperelastic modelling of ligaments and
tendons based on the geometrical arrangement of their fibrils is derived. The
distribution of the crimp angles of the fibrils is used to determine the
stress-strain response of a single fascicle, and this stress-strain response is
used to determine the form of the strain energy function, the parameters of
which can all potentially be directly measured via experiments - unlike those
of commonly used strain energy functions such as the Holzapfel-Gasser-Ogden
(HGO) model, whose parameters are phenomenological. We compare the new model
with the HGO model and show that the new model gives a better match to existing
stress-strain data for human patellar tendon than the HGO model, with the
average relative error in matching this data when using the new model being
0.053 (compared with 0.57 when using the HGO model), and the average absolute
error when using the new model being 0.12 MPa (compared with 0.31 MPa when
using the HGO model).
