Continuum Mechanics and Thermodynamics

, Volume 31, Issue 3, pp 607–626 | Cite as

A variational homogenization approach applied to the multiscale analysis of the viscoelastic behavior of tendon fascicles

  • Thiago André Carniel
  • Eduardo Alberto FancelloEmail author
Original Article


This work presents a variational homogenization approach based on representative volume elements (RVE) in order to investigate the macro- and microviscoelastic behavior of tendon fascicles. A three-dimensional hexagonal–helicoidal finite element RVE is proposed to properly account for the morphology of tendon fascicles observed in serial block-face scanning electron microscopy. Two material phases (collagen fibers and cells) comprising three finite strain variational viscoelastic models (fibrils, matrix of fibers and cells) compose the proposed multiscale model. The material parameters of the micromechanical models were identified with the aid of atomic force microscopy experiments extracted from the literature. A set of multiscale simulations of tensile tests under physiological strain amplitudes were performed, providing the following results. Firstly, numerical predictions corroborate experimental findings: collagen fibrils are the main load-bearing structures of tendons; the cellular matrix contributes neither to the stiffness nor to the energy dissipation of tendons. Secondly, the model brings insights about microscale mechanics of tendon fascicles not completely understood: prediction of uncoiling of fibers during axial loads which may explain the large apparent Poisson ratios and fluid loss, and significant strain localization in cells, which may lead to important mechanotransduction mechanisms. Moreover, the distribution of dissipated power became available, pointing out the fibrils as the main source of dissipation of fascicles under high macroscopic strain rates and during the unloading phase in cyclic regimes.


Tendon Soft tissues Multiscale Homogenization Viscoelastic model Finite element method 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.GRANTE - Department of Mechanical EngineeringFederal University of Santa CatarinaFlorianópolisBrazil
  2. 2.LEBm - University HospitalFederal University of Santa CatarinaFlorianópolisBrazil

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