Open source MATLAB code for the linear elastic analysis of heterogeneous materials and structures by using the Extended Multiscale Finite Element Method (EMsFEM)
%%% A detailed description of the code can be viewed in the paper:
%%% Hui Liu, Dongsheng Yang, Jingkai Wu, Yonggang Zheng, Hongwu Zhang. An Open-Source MATLAB Implementation for elastic analysis of heterogeneous materials using the Extended Multiscale Finite Element Method. International Journal for Multiscale Computational Engineering, 2021, DOI: 10.1615/IntJMultCompEng.2021039777
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Extended Multiscale Finite Element Method (EMsFEM) has been more and more widely used in the multiscale analysis of the mechanical properties of heterogeneous materials and structures, since it has no assumptions of scale separation and periodicity compared to the asymptotic homogenization method and the representative volume element (RVE) method. To further facilitate the promotion and application of the EMsFEM, this paper discourses the basic ideas, principles and implementations of this method in detail, and releases the corresponding MATLAB code for free use by researchers. Based on the work of this paper, scholars can carry out further researches on different multiscale computation problems. Both the oversampling technique and periodic boundary conditions are provided to construct the numerical shape function, and their implementation processes are also introduced in detail. In addition, some typical numerical examples are given for verifying the effectiveness of the EMsFEM.