A model for the biaxial dynamic bending of unbonded flexible pipes

•A model for the biaxial dynamic bending of unbonded flexible pipes is presented.•An incremental method based on an operator splitting and return-mapping algorithm is used to obtain the tension gradient.•Besides stick-slip behavior, several other aspects are included, such as bending induced tension and shear deformations.•Poisson's effect and the changes of wire effective torsion and curvature increments after slip occurs are also considered.•The model’s ability to evaluate the armor wire stresses can serve as the basis for a fatigue analysis of those wires.

An analytical model is given to investigate the behavior of unbonded flexible pipes under biaxial dynamic bending. The stick-slip conditions of each wire are studied in the framework of incremental analysis by an operator splitting of the time step into a stick-state prediction and a slip-state correction step. The tension gradient is calculated using the classical return-mapping algorithm and the obtained tension gradients are integrated numerically to find the axial tension by imposing appropriate boundary conditions. From the axial tension the bending moments with respect to the principal bending axes of the pipe are obtained. Poisson's effect, bending induced tension in the wire, shear deformations of the supporting plastic layer and the changes of the effective torsion and curvature increments of the wire after slip occurs are taken into account in the model. The results of bending moment–curvature relationship from this model are compared with the test data from simple bending and good correlations are found. The comparison of the biaxial bending moment results between this model and the available model also shows good agreement.