Résumé
The present work is devoted to the microbuckling analysis of long fiber composites. A multiscale finite element method (FE2) is combined with the asymptotic numerical method (ANM) to study the elastoplastic instability which may occur in structures at both macroscopic and microscopic scales. The fiber is described by a linear material constitutive law, while the matrix phase is described by a nonlinear Ramberg-Osgood relationship. The stress field is then obtained via the total mechanical strain without any history dependence. Large strains are considered, which induce geometrical nonlinearities in both cases. The ANM framework allows obtaining complex response curves involving limit points in loading and displacement to be obtained. In the present path following procedure, adjustment of the step length is naturally automatic because the validity range of the asymptotic solution is a posteriori estimated depending on the local nonlinearity of the response branches. Numerical examples show the effectiveness of the proposed approach by investigating microscopic and macroscopic instabilities of long fiber composite structures in compression.