Uniaxial poroelastic tendon model with crimped fibre recruitment reveals hysteresis
Abstract
Fibre recruitment plays an important role in tendon. Due to their large water content, a popular modelling approach for tendons is poroelasticity. Within this framework some tendon studies have included fibres, though none have included crimped fibre recruitment. We present a one dimensional poroelastic model in which the solid skeleton is composed of a soft neo-Hookean background matrix and crimped fibrils which do not bear load (FIB model). As the tissue is stretched, fibrils are straightened and contribute to load bearing. The fibre-reinforced tissue is compared to a tissue with a purely neo-Hookean (NH) skeleton in response to a uniaxial constant applied load (loading) and release of the load (unloading). The system dynamics are governed by a diffusion equation where the diffusion coefficient depends on stiffness. Within tendon parameter ranges, the FIB model is softer than the NH model, and so approaches steady state more slowly during loading. The presence of stiff, crimped fibrils increases bulk extension without excessively straining the fibrils, providing a natural protection mechanism for the tendon's structural components to load, in agreement with experiments. During unloading, the FIB model is much slower to relax as the tissue softens due to fibril re-crimping. This asymmetry in loading and unloading manifests as a hysteresis loop in the stress-strain curve averaged over the tendon. The hysteresis is reduced with increasing applied load. To the authors' knowledge, the finding of hysteresis within this framework is novel. The inclusion of fibrils allows for clearer biological interpretation and potential comparison to data. While the stress law employed in this study is bespoke for the application at hand by accounting for crimp and fibril recruitment, other fibril constitutive laws can readily be considered and incorporated into this framework.
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BibTeX
@misc{godard2026uniaxial,
title = {{Uniaxial poroelastic tendon model with crimped fibre recruitment reveals hysteresis}},
author = {Zoe C. Godard and Sarah L. Waters and Derek E. Moulton},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.24393},
eprint = {2606.24393},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.24393},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uniaxial poroelastic tendon model with crimped fibre recruitment reveals hysteresis
AU - Zoe C. Godard
AU - Sarah L. Waters
AU - Derek E. Moulton
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2606.24393
UR - https://arxiv.org/abs/2606.24393
AB - Fibre recruitment plays an important role in tendon. Due to their large water content, a popular modelling approach for tendons is poroelasticity. Within this framework some tendon studies have included fibres, though none have included crimped fibre recruitment. We present a one dimensional poroelastic model in which the solid skeleton is composed of a soft neo-Hookean background matrix and crimped fibrils which do not bear load (FIB model). As the tissue is stretched, fibrils are straightened and contribute to load bearing. The fibre-reinforced tissue is compared to a tissue with a purely neo-Hookean (NH) skeleton in response to a uniaxial constant applied load (loading) and release of the load (unloading). The system dynamics are governed by a diffusion equation where the diffusion coefficient depends on stiffness. Within tendon parameter ranges, the FIB model is softer than the NH model, and so approaches steady state more slowly during loading. The presence of stiff, crimped fibrils increases bulk extension without excessively straining the fibrils, providing a natural protection mechanism for the tendon's structural components to load, in agreement with experiments. During unloading, the FIB model is much slower to relax as the tissue softens due to fibril re-crimping. This asymmetry in loading and unloading manifests as a hysteresis loop in the stress-strain curve averaged over the tendon. The hysteresis is reduced with increasing applied load. To the authors' knowledge, the finding of hysteresis within this framework is novel. The inclusion of fibrils allows for clearer biological interpretation and potential comparison to data. While the stress law employed in this study is bespoke for the application at hand by accounting for crimp and fibril recruitment, other fibril constitutive laws can readily be considered and incorporated into this framework.
ER -