On a three-dimensional constitutive model for history effects in skeletal muscles

  • Robert Seydewitz
  • Tobias Siebert
  • Markus BölEmail author
Original Paper


An exceptional property of skeletal muscles that distinguishes them from other soft tissues is their ability to contract by generating active forces, which in turn are initiated by an electrochemical trigger. Some of these so-called active material properties are generally characterised using isometric contraction experiments at various muscle lengths. In this context, experimental observations revealed that unlike the widespread assumption in muscle modelling, reaction forces indeed depend on so-called history effects, which can be classified into force enhancement and force depression. For the experimental settings of force enhancement, two subsequent isometric contractions are interrupted by an isokinetic extension. The isometric reaction force is increased after the isokinetic extension with respect to a reference measurement, while in the case of force depression, isokinetic shortening is responsible for forces below a certain isometric reference measurement. Most theoretical investigations of force enhancement and force depression use one-dimensional models to simulate the force response considering muscle deformation to be homogeneous. In contrast, the aim of the present study is to analyse history effects in skeletal muscle tissue using a three-dimensional geometry model of the whole muscle–tendon unit. Therefore, a purely phenomenological approach is presented. The model is implemented in the finite element framework to analyse history effects for the boundary value problem of the entire three-dimensional muscle–tendon geometry. The constitutive model shows good agreement with the experimental data. Furthermore, the simulations reveal information about the inhomogeneous stretch distributions within the muscle tissues.


Skeletal muscle Force depression Force enhancement Muscle properties Three-dimensional modelling Parameter identification 



This work was supported by the Deutsche Forschungsgemeinschaft (DFG) under Grants BO 3091/4-1, 2 and SI 841/3-1, 2. The authors like to thank Dr. Kay Leichsenring for fruitful discussions.


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Authors and Affiliations

  1. 1.Institute of Solid MechanicsTechnische Universität BraunschweigBraunschweigGermany
  2. 2.Institute of Sport and Motion ScienceUniversity of StuttgartStuttgartGermany

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