Multiple grid for computing the composite behavior with spectral method

The local and overall nonlinear responses of composites are generally calculated by the Finite Element Method (FEM). This traditional FEM method requires meshing geometry and assembling stiffness matrix. Spectral method based on Fast Fourier Transforms directly using real microstructure images can avoid these steps. Composites with complex structure can be discretized into a set of regular grids. But grids cannot describe interface between fiber and matrix exactly. To circumvent this difficulty, we restructure the original pixels into three types: virgin matrix grid, virgin fiber grid and interface grid. The interface grid effective stiffness is determined approximately by using the laminate rules and homogenization technique. The results show that this approach can be used to estimate the effective material properties of many complex microstructures. Comparing with classical FFT-based method, multiple interface grids can improve the local solution quality and the accuracy of the predicted effective elastic properties.