An adaptive multiscale method for strain localization analysis of 2D periodic lattice truss materials

Abstract

The numerical analysis of truss materials and structures often involves a huge number of degrees of freedom leaving the analysis intractable when using the traditional numerical methods. To reduce the computational costs and avoid the macroscopic grid sensitivity, an adaptive multiscale technique is developed for strain localization analysis of periodic lattice truss materials. With the evolution of microscopic state variables, the full macro-scale model is adaptively transformed into a multiscale model, where the localized zone is automatically detected and resolved on a fine-scale by the direct finite element method; at the same time, for the other subregions, the coarse-scale model is adopted and is resolved by the extended multiscale finite element method. To achieve computational efficiency, a displacement gradient-based mesh indicator is proposed for the adaptive scheme to identify the fine-scale subregions during the computational process. The two different scales are then bridged at the interfaces by means of the multiscale base functions, which are constructed numerically and can efficiently capture the small-scale features of a coarse element. Several typical numerical examples are calculated and the results are compared to the reference solutions to demonstrate the validity of the method proposed.

Keywords:

• adaptive multiscale technique
• strain localization
• truss material
• scale bridging

Acknowledgments

The supports of the National Natural Science Foundation (11072051, 11232003, 11272003, 51021140004), the 111 Project (B08014) and the National Key Basic Research Special Foundation of China (2010CB832704) are gratefully acknowledged.