Biomechanics and Modeling in Mechanobiology

, Volume 11, Issue 3, pp 505–517

An insight on multiscale tendon modeling in muscle–tendon integrated behavior

Original Paper

DOI: 10.1007/s10237-011-0329-8

Cite this article as:
Maceri, F., Marino, M. & Vairo, G. Biomech Model Mechanobiol (2012) 11: 505. doi:10.1007/s10237-011-0329-8


This paper aims to highlight the need for a refined tendon model to reproduce the main mechanical features of the integrated muscle–tendon unit (MTU). Elastic nonlinearities of the tendon, both at the nano and microscale, are modeled by a multiscale approach, accounting for the hierarchical arrangement (from molecules up to the fibers) of the collagen structures within the tissue. This model accounts also for the variation of tendon stiffness due to physical activity. Since the proposed tendon model is based on tissue-structured histology, the training-driven adaptation laws are directly formulated starting from histological evidences. Such a tendon description is integrated into a viscoelastic Hill-type model of the whole MTU. A fixed-end contraction test is numerically simulated, and results based on both linear and nonlinear tendon elastic model are compared. Sound and effective time-histories of muscle contractile force and fiber length are obtained only accounting for tendon elastic nonlinearities, which allow to quantitatively recover some experimental data. Finally, proposed numerical results give clear indications toward a rational explanation of the influence of tendon remodeling induced by physical activity on muscular contractile force.


Hill-type modeling of muscle-tendon unitTendon mechanicsTendon nonlinear multiscale modelingNanomechanics of collagen moleculeFixed-end contractionTraining effects on tendon mechanics

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of Rome “Tor Vergata”RomeItaly