A Fourier-related FE2 multiscale model for instability phenomena of long fiber reinforced materials

This work aims to develop a computationally efficient multiscale model to accurately simulate and analyze the instability phenomena of long fiber reinforced composites. The multilevel finite element method (FE2) based on the homogenization theory is adopted to realize the real-time interaction between the microscopic and the macroscopic levels. To increase the computational efficiency in the microscopic level and control the nonlinear calculations, the Fourier-related analysis, is carried out on the representative volume elements (RVEs), where all fast varying unknowns are replaced by slowly varying unknowns. The established nonlinear multiscale system is solved by the Asymptotic Numerical Method (ANM), which is more reliable and less time consuming than other classical iterative methods. This model is used to study the structural instability and the fiber micro-buckling of long fiber reinforced composites. The effects of fiber wavelength on the buckling and post-buckling of macro structure are discussed.