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An Anisotropic Micro-Sphere Approach Applied to the Modelling of Soft Biological Tissues

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • A. Menzel

    (Institute of Mechanics, Department of Mechanical Engineering, TU Dortmund
    Lund University, Division of Solid Mechanics)

  • T. Waffenschmidt

    (Institute of Mechanics, Department of Mechanical Engineering, TU Dortmund)

  • V. Alastrué

    (University of Zaragoza, Group of Structural Mechanics and Materials Modelling, Aragón Institute of Engineering Research (I3A))

Abstract

A three-dimensional model for the simulation of anisotropic soft biological tissues is discussed. The underlying constitutive equations account for large strain deformations and are based on a hyper-elastic form. As various soft biological tissues are nearly incompressible, we adopt the classical volumetric-isochoric split of the strain energy density. While its isotropic part is chosen to take a standard neo-Hookean form, its anisotropic part is determined by means of the so-called micro-sphere model. In this regard, physically sound one-dimensional constitutive models – as for instance the worm-like chain model – can be used and straightforwardly be extended to the three-dimensional case. As a key aspect, the micro-sphere model is extended to further capture remodelling. Such deformation-induced anisotropy is introduced by setting up evolution equations for the integration directions used to perform numerical integrations on the unit-sphere. The particular model proposed captures orthotropic material behaviour and additionally accounts for saturation effects combined with a visco-elasticity-type time-dependent anisotropy evolution.

Suggested Citation

  • A. Menzel & T. Waffenschmidt & V. Alastrué, 2010. "An Anisotropic Micro-Sphere Approach Applied to the Modelling of Soft Biological Tissues," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 637-644, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_68
    DOI: 10.1007/978-3-642-11795-4_68
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