Zoe C. Godard | Searcharxiv

arXiv2026

Uniaxial poroelastic tendon model with crimped fibre recruitment

Fibre recruitment plays an important role in tendon and other biological soft tissue mechanics. 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 crimped fibrils allows the tendon to stretch further without excessively straining the fibrils or the NCM, 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. 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.

physics.bio-ph↗

arXiv2025

Cyclic loading of a heterogeneous non-linear poroelastic material

Cyclic loading is a common feature in poroelastic systems, the material response depending non-trivially on the exact form of boundary conditions, pore structure, and mechanical properties. The situation becomes more complex when heterogeneity is introduced in the properties of the poroelastic material, yet heterogeneity too is common in physical poroelastic structures. In this paper, we analyse the behaviour of a soft porous material in response to a uniaxial cyclic stress or displacement, with a focus on understanding how this response is affected by continuous heterogeneity in the stiffness or permeability. Our work is motivated by observed altered material properties of the diseased tendon, but the framework we develop and analyse is generically applicable. We construct a one-dimensional non-linear poroelastic model, assuming Darcy flow through the pores of the solid skeleton which we assume has neo-Hookean elasticity. The system is driven by an applied uniaxial cyclic stress or a uniaxial cyclic displacement at one boundary. Heterogeneity in the stiffness or permeability profile is imposed via a Gaussian bump function. By exploring a range of loading frequencies together with magnitudes and locations of heterogeneity, we characterise the effect of heterogeneity on the response of the material, and show that the response of the system to an applied stress is qualitatively distinct from the response to an applied displacement. Our analysis of this simple model provides a foundation for understanding how heterogeneity affects the poroelastic response to cyclic loading.

cond-mat.soft↗