Investigation of FGM membrane wrinkling using reduced models based on a multi-scale method

In this article, we show that the reduced model proposed in our recent article to study the wrinkling of homogeneous elastic membranes does not reproduce the wrinkling observed in the case of an FGM-type composite membrane. New reduced models are then proposed to investigate the wrinkling of membranes made from Functionally Graded Materials (FGM). We examine, by this way, the influence of material functional parameters on determining the critical load and post-critical behavior under different loads. These reduced models, created using a multi-scale method based on Fourier series with slowly varying coefficients, enrich the reference model. In addition, these reduced models also allow us to significantly decrease the computation time and the number of finite elements compared to the complete model. The robustness of these reduced models is demonstrated in the case of wrinkling of membranes modeled by very thin shells, which are discretized using DKT18-type finite elements as described in literature. The resulting nonlinear problems are solved using a High-Order Continuation Method (HOCM).