Bend stiffener nonlinear viscoelastic time domain formulation

Abstract

Bend stiffeners are conical polyurethane structures used in the offshore industry to ensure a smooth transition in the upper connection of flexible risers with the floating production unit. The polyurethane employed for bend stiffeners present a nonlinear viscoelastic response that is highly dependent on the loading rate and temperature. This may lead to different flexible riser response when compared to elastic or hyperelastic material modeling. In order to quantify this effect, tensile and relaxation tests are carried out to characterize the nonlinear time dependent mechanical behavior of the polyurethane. A constitutive equation based on the modified superposition method is then presented and a procedure for material identification proposed. A numerical scheme using the state variable approach is formulated for the nonlinear viscoelastic constitutive equation finite element implementation. The top connection system, consisting of a bend stiffener and a flexible pipe segment, is represented by a large displacement beam model accounting for geometrical and material nonlinearities. A case study is carried out to compare the system curvature response calculated for the nonlinear viscoelastic and hyperelastic (Marlow strain energy potential) bend stiffener subjected to harmonic loading conditions at different frequencies. The results show the importance of bend stiffener strain rate dependency on the riser curvature response.