A model reduction method for the post-buckling analysis of cellular microstructures

Multiscale finite element models are useful in some applications such as biological tissues or foams to determine the effective properties of the solids. In this paper, a model reduction method is proposed, that is applied in the post-buckling regime of cellular microstructures. The proposed approach combines a perturbation technique with the proper orthogonal decomposition (POD). The computation of finite series leads to an efficient continuation method, which enables handling limit points and instabilities naturally. Each term of the series is itself developed using POD. The size of the problems to be solved is thus drastically reduced. Computations involving two and three-dimensional microstructures in compression enable to evaluate the potential of the technique in view of applications to multiscale analyses.