Micromechanical poroelastic finite element and shear-lag models of tendon predict large strain dependent Poisson's ratios and fluid expulsion under tensile loading

Acta Biomater. 2015 Aug;22:83-91. doi: 10.1016/j.actbio.2015.04.035. Epub 2015 Apr 29.

Abstract

As tendons are loaded, they reduce in volume and exude fluid to the surrounding medium. Experimental studies have shown that tendon stretching results in a Poisson's ratio greater than 0.5, with a maximum value at small strains followed by a nonlinear decay. Here we present a computational model that attributes this macroscopic observation to the microscopic mechanism of the load transfer between fibrils under stretch. We develop a finite element model based on the mechanical role of the interfibrillar-linking elements, such as thin fibrils that bridge the aligned fibrils or macromolecules such as glycosaminoglycans (GAGs) in the interfibrillar sliding and verify it with a theoretical shear-lag model. We showed the existence of a previously unappreciated structure-function mechanism whereby the Poisson's ratio in tendon is affected by the strain applied and interfibrillar-linker properties, and together these features predict tendon volume shrinkage under tensile loading. During loading, the interfibrillar-linkers pulled fibrils toward each other and squeezed the matrix, leading to the Poisson's ratio larger than 0.5 and fluid expulsion. In addition, the rotation of the interfibrillar-linkers with respect to the fibrils at large strains caused a reduction in the volume shrinkage and eventual nonlinear decay in Poisson's ratio at large strains. Our model also predicts a fluid flow that has a radial pattern toward the surrounding medium, with the larger fluid velocities in proportion to the interfibrillar sliding.

Keywords: Extracellular matrix; Finite element modeling; Poisson’s ratio; Poroelasticity; Tendon.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Biomechanical Phenomena
  • Elasticity
  • Finite Element Analysis*
  • Models, Biological*
  • Porosity
  • Rheology
  • Tendons / physiology*
  • Tensile Strength*