A uniform multiscale method for 3D static and dynamic analyses of heterogeneous materials

In this paper, a uniform multiscale method is developed for 3D static and dynamic analyses of heterogeneous materials based on our previous work (H.W. Zhang, H. Liu, J.K. Wu, International Journal for Numerical Methods in Engineering 93 (2013) 714–746). A new 3D multi-node coarse element is provided to simulate the complex deformation and the approach is elaborated to construct the displacement base functions numerically. For the dynamic problems, to consider the effect of the interior forces of the structure, the mode base functions are introduced for improving the computational accuracy. In addition, the orthogonality between the displacement and mode base functions indicates that this proposed multiscale method can be used for the static and dynamic analyses uniformly. Finally, several typical numerical examples are carried out to verify the validity and high efficiency of this multiscale method by comparison with the reference solutions.