The objective of this paper is to assess the efficiency of the asymptotic numerical method to solve problems coupling various nonlinearities. The 3D hemispherical stretching of a circular sheet, that involves geometrical, material and red unilateral contact nonlinearities is chosen as an example. An elastoplastic model based on the plasticity deformation theory is adopted. The structural discretization is performed by a shell finite element well adapted for problems involving large displacements and large rotations. The unilateral contact problem is identified to boundary conditions which are replaced by force-displacement relations and solved using a special algorithm. Comparisons with results obtained by the help of an industrial code establish the interest and the performance of the present method.
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