Biomechanics and Modeling in Mechanobiology

, Volume 3, Issue 3, pp 147–171 | Cite as

Modelling of anisotropic growth in biological tissues

A new approach and computational aspects
  • A. MenzelEmail author
Original Paper


In this contribution, we develop a theoretical and computational framework for anisotropic growth phenomena. As a key idea of the proposed phenomenological approach, a fibre or rather structural tensor is introduced, which allows the description of transversely isotropic material behaviour. Based on this additional argument, anisotropic growth is modelled via appropriate evolution equations for the fibre while volumetric remodelling is realised by an evolution of the referential density. Both the strength of the fibre as well as the density follow Wolff-type laws. We however elaborate on two different approaches for the evolution of the fibre direction, namely an alignment with respect to strain or with respect to stress. One of the main benefits of the developed framework is therefore the opportunity to address the evolutions of the fibre strength and the fibre direction separately. It is then straightforward to set up appropriate integration algorithms such that the developed framework fits nicely into common, finite element schemes. Finally, several numerical examples underline the applicability of the proposed formulation.


Residual Stress Fibre Direction Structural Tensor Fibre Strength Free Helmholtz Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Chair of Applied Mechanics, Department of Mechanical and Process EngineeringUniversity of KaiserslauternKaiserslauternGermany

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