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

Biomech Model Mechanobiol. 2021 Feb;20(1):323-337. doi: 10.1007/s10237-020-01388-3. Epub 2020 Oct 3.

Abstract

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.

Keywords: Cutting test; Efficient numerics; Fibre-reinforced composites; Finite strain viscoelasticity; Opening angle approach; Pre-stresses.

MeSH terms

  • Arteries / pathology*
  • Arteries / physiopathology*
  • Biomechanical Phenomena
  • Computer Simulation
  • Elasticity
  • Finite Element Analysis
  • Nonlinear Dynamics*
  • Pressure
  • Stress, Mechanical*
  • Thermodynamics
  • Viscosity