Due to the manufacturing process, defects such as delamination or matrix cracking are present in composite pipes used in satellite applications. To determine if these parts must be rejected, an experimental approach is used at the present time. The purpose of this study is to provide the Alcatel Alenia Space engineers with a dedicated numerical decision-making tool and, thus, reduce both the cost of verification and the number of rejected pipes. The behavior of the damaged pipes is modeled at the scale of the elementary ply with the model described in [
] following the work of [
]. A major issue at this scale is the computational cost, because the ply thickness is 0.2 mm. This leads to solve a several million degrees of freedom problem to catch edge effects. The proposed strategy is divided in two steps. First, due to the damage location, the exact beam theory developed in [
] is used to build the elastic solution at the middle of the pipe [
] while the ends are treated using a fine non linear modeling. Second, the elastic problem defined on the end zone and used in a non linear resolution scheme is solved using special finite elements based on Fourier expansions in the hoop direction. This allows, by the use of a preconditioned conjugate gradient method, to uncouple the resolution of the non axisymmetric problems [
]. A major question is then tackled, it is concerning the expansion order needed to get a given quality in the hoop description. Industrial cases of several millions of degrees of freedom with defects have been treated in elasticity with a prototype code developed in Matlab.