Introduction of shear warping in fibre beam elements for the computation of the nonlinear behaviour of concrete beams

The present paper deals with modelling the nonlinear behaviour of concrete using the fibre element method. Proved to be efficient for slender structural elements mainly subject to normal stresses, the method lacks in accuracy when modelling the effect of shear. The present contribution proposes to enhanced a Timoshenko fibre beam element by adding shear warping deformations in the formulation. Transverse shear as well as torsion warping is taken into account, enabling the computation of the response to a complex loading. Warping degrees of freedom are computed simultaneously with the beam degrees of freedom by a fully implicit solution procedure. Concrete is modelled using a 3D damage model. Due to the coupling of warping and global beam degrees of freedom, the warping displacements in the beam element can evolve with the evolution of concrete damage. The beam element enhancement is validated at the cross-section scale considering a linear elastic behaviour. Enhanced beam elements are then used to model experimentally-tested structural elements. Both the linear and non-linear parts of the structural response are investigated.