Multiscale method for mechanical analysis of heterogeneous materials with polygonal microstructures

Abstract

An extended multiscale finite element method is developed to solve the mechanical behaviors of heterogeneous materials with randomly distributed polygonal microstructure. A type of rational oversampling technique is imposed to calculate the oscillatory boundary conditions for the construction of multiscale base functions. To improve the accuracy of the method, a mixed extended multiscale finite element method, which combines the extended multiscale finite elements method and the traditional finite element method into a same model, is developed. In the method, the regions with multiscale features are modeled by the multiscale coarse-grid, while the region without multiscale features or the domains that need a high-precision computation are directly meshed by the general finite elements. Two applications of the multiscale methods on heterogeneous wood structure and the closed liquid cell materials are presented in numerical examples. The results indicate that the multiscale methods developed in this paper have high accuracy and efficiency.