Fig 1.
An illustration of the viscoelastic model representing the collagen fibres.
E1, E2, k1, k2 and η are system constants, εf stands for the total fibre strain, εv is the strain in the dash pot and εe is the strain in the spring in the Maxwell element.
Fig 2.
A) Mesh and boundary conditions. B) The experimental loading protocol cycles 1–3 for all 9 tendons interpolated over 2π for each load cycle (grey). The average loading protocol for cycles 1–3 (red). C) The loading protocols for cycle 1–3 for all 9 tendons in the time-domain (grey) illustrate the variability among experimental specimens. The average loading protocol for cycles 1–3 in time-domain (red).
Fig 3.
A schematic picture showing the optimisation procedure.
Fig 4.
The new poroviscoelastic model fitted to experimental data from cycle 1–3 of the tensile tests on rat Achilles tendons. The best (A) material model fit (RMS = 0.42) and the worst (B) material model fit (RMS = 1.02).
Table 1.
The optimised model parameters for all 9 specimen-specific finite element models based on cycle 1–3.
Fig 5.
The optimised result when the material model is fitted to the average tendon model and the average loading protocol. A) Loading cycle 1–3, RMS = 0.84 and B) during later loading cycles (cycle 10–12), RMS = 0.41.
Table 2.
The optimised model parameters for the average tendon model based on cycle 1–3 and 10–12.
Fig 6.
The strain-stiffening behaviour captured by the poroviscoelastic model where the Achilles tendons subjected to higher strain-rates exhibit a stiffer and more brittle behaviour than when subjected to slower strain-rates.
Fig 7.
Stress-relaxation response of the Achilles tendon, as predicted by the material model. Higher strains result in reduced relaxation compared to lower strain magnitudes (A), and demonstrate a slower relaxation rate, as illustrated in the log-log plot (B).
Fig 8.
A) Model prediction of the creep behaviour in Achilles tendons when subjected to different stress magnitudes. B) The log-log plot shows almost no stress-dependent creep rate behaviour.
Fig 9.
Contribution of tissue constituents.
A) The stress in the collagen fibres and B) the stress in the non-fibrillar matrix, during one load cycle. C) Fluid velocities in the tendon during one load cycle (output from highlighted element at the centre edge of the tendon mesh, see Fig 2A). The dip in fluid velocity is an effect of the boundary condition, which creates a propagating wave through the tendon.