Abstract: Smoothed Multiscale Finite Element Method (SMsFEM) is proposed to solve the problems associated with heterogeneous and multiscale materials. SMsFEM is used to study the fliud flow in fractured madia with a dual porosity model. Using the global fine-scale solution at initial time to determine the boundary conditions of the basis function, local information of material heterogeneity and coupled global information, such as fluid flow in porous and fractured media, are simultaneously reflected in the multiscale finite element basis functions. As a result, an accurate solution can be achieved in the coarse scale. SMsFEM introduces the strain smoothing technique into conventional Multiscale Finite Element Method (MsFEM), therefore, simplifies the assembly of the macro matrix and overcomes the overly-stiff phenomenon existing in the traditional finite element method. Simulation results indicate that the proposed SMsFEM is highly consistent with the fine-scale solutions from standard finite element method. It is also demonstrated that SMsFEM has better efficiency and accuracy than MsFEM.

Key words: solid mechanics, smoothed multiscale finite element method, dual porosity model, multiscale finite element method, strain smoothing technique