Geometrically nonlinear modelling of pre-stressed viscoelastic fibre-reinforced composites with application to arteries

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Mechanical behaviour of pre-stressed fibre-reinforced composites is modelled in a geometrically exact setting. A general approach which includes two different reference configurations is employed: one configuration corresponds to the load-free state of the structure and another one to the stress-free state of each material particle. The applicability of the approach is demonstrated in terms of a viscoelastic material model; both the matrix and the fibre are modelled using a multiplicative split of the deformation gradient tensor; a transformation rule for initial conditions is elaborated and specified. Apart from its simplicity, an important advantage of the approach is that well-established numerical algorithms can be used for pre-stressed inelastic structures. The interrelation between the advocated approach and the widely used "opening angle" approach is clarified. A full-scale FEM simulation confirms the main predictions of the "opening angle" approach. A locking effect is discovered: in some cases the opening angle of the composite is essentially smaller than the opening angles of its individual layers. Thus, the standard cutting test typically used to analyse pre-stresses does not carry enough information and more refined experimental techniques are needed.

Original languageEnglish
Pages (from-to)323-337
Number of pages15
JournalBiomechanics and Modeling in Mechanobiology
Issue number1
Publication statusPublished - Feb 2021


  • Pre-stresses
  • Finite strain viscoelasticity
  • Fibre-reinforced composites
  • Cutting test
  • Opening angle approach
  • Efficient numerics


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