= \frac{\rho^\mathrm{c}_{0}}
{\rho^\mathrm{c}_{0_{\mathrm{ini}}}} \be \otimes \be$, with $\rho^\mathrm{c}_{0_{\mathrm{ini}}}$ denoting the initial concentration of collagen at the point.

The mechanical response of tendons in tension is determined primarily by their dominant structural component: highly oriented fibrils of collagen. In our preliminary formulation, the strain energy density for collagen has been obtained from hierarchical multi-scale considerations based upon an entropic elasticity-based worm-like chain (WLC) model [@KratkyPorod:49]. The WLC model has been widely used for long chain single molecules, most prominently for DNA [@MarkoSiggia:95; @Riefetal:97; @Bustamanteetal:2003], and recently for the collagen monomer [@Sunetal:2002]. The central parameters of this model are the chain’s contour length, $L$, and persistence length, $A$. The latter is a measure of its stiffness and given by $A = \chi/k\theta$, where $\chi$ is the bending rigidity, $k$ is Boltzmann’s constant and $\theta$ is the temperature. See @LandLif for general formulation of statistical mechanics models of long chain molecules.

To model a collagen network structure, the WLC model has been embedded as a single constituent chain of an eight-chain model [@Bischoffetal:2002; @Bischoffetal1:2002], depicted in . Homogenisation via averaging then leads to a continuum Helmholtz free energy function, $\hat{\psi}^\mathrm{c}$:[^9]

$$\begin{split}
\rho^\mathrm{c}_{0}\hat{\psi}^\mathrm{c} (\bF^{\mathrm{e}^\mathrm{c}},\rho^\mathrm{c}_{0})
&= \frac{N k \theta}{4 A}\left(\frac{r^2}{2L} + \frac{L}{4(1-r/L)} -
\frac{r}{4}\right)\\ & 