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Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 6, pp 1773–1790 | Cite as

A chemo-mechanical model for osmo-inelastic effects in the annulus fibrosus

  • Amil Derrouiche
  • Fahmi ZaïriEmail author
  • Fahed Zaïri
Original Paper

Abstract

The annulus fibrosus exhibits complex osmotic and inelastic effects responsible for unusual transversal behavior with a Poisson’s ratio higher than 0.5 in fibers plane and negative (i.e., auxetic) in lamellae plane. In this paper, we present a new chemo-mechanical approach for the intrinsic osmo-inelastic response of the annulus fibrosus in relation to the microstructure of the layered reinforced soft tissue, the biochemical environment and the mechanical loading conditions. The constitutive model introduces the coupling between the deformation-induced inelastic stress in the tangled extracellular matrix and the stress-free swelling due to internal fluid content variation by osmosis. The proposed formulation is implemented into a finite element code, and numerical simulations on annulus specimens, including explicitly lamellae and interlamellar zones, are presented. To illustrate the capability of the approach to capture experimental observations quantitatively, the simulated results are compared to experimental results obtained by monitoring the full-field strain in annulus specimens using digital image correlation method. Some material constants are found by matching the free swelling in a water bath with different salt concentrations, and others are found by matching tensile results in terms of loading–unloading stress–stretch curve and transversal behavior. The constitutive model is found to successfully capture the variations in osmolarity and strain-rate conditions (both statistically significant, p < 0.05) on the intrinsic response and the auxeticity. The stress/strain patterns in the model simulation provide valuable insights into the role of the interlamellar zone in the osmo-inelastic mechanisms.

Keywords

Annulus fibrosus Constitutive modeling Osmo-inelastic coupling Transversal behavior Finite element analysis 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Civil Engineering and geo-Environmental Laboratory (EA 4515 LGCgE)Lille UniversityLilleFrance
  2. 2.Ramsay Générale de SantéHôpital privé Le BoisLilleFrance

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