Numerical derivation of constitutive models for unbonded flexible risers

Abstract

In this paper a new constitutive model for flexible risers is proposed and a procedure for the identification of the related input parameters is developed using a multi-scale approach. The constitutive model is formulated in the framework of an Euler–Bernoulli beam model, with the addition of suitable pressure terms to the generalized stresses to account for the internal and external pressures, and therefore can be efficiently used for large-scale analyses. The developed non-linear relationship between generalized stresses and strains in the beam is based on the analogy between frictional slipping between different layers of a flexible riser and frictional slipping between micro-planes of a continuum medium in non-associative elasto-plasticity. Hence, a linear elastic relationship is used for the initial response in which no-slip occurs; an onset-slip function is introduced to define the ‘no-slip’ domain, i.e. the set of generalized stresses for which no slip occurs; a non-associative rule with linear kinematic hardening is used to model the full-slip phase. The results of several numerical simulations for a riser of small-length, obtained with a very detailed (small-scale) non-linear finite-element model, are used to identify the parameters of the constitutive law, bridging in this way the small scale of the detailed finite-element simulations with the large scale of the beam model. The effectiveness of the proposed method is validated by the satisfactory agreement between the results of various detailed finite-element simulations for a short riser, subject to internal and external uniform pressure and uniform cyclic bending loading, with those given by the proposed constitutive law.