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Abstract

We present a new multiscale method for locally-nonperiodic heterogeneous materials. By decomposing them into periodic part and nonperiodic part, multiscale finite element model is constructed in a straightforward manner. The periodic part is appropriately coarse-grained through homogenization process and the nonperiodic part is retained to capture the localizing phenomena of materials. For seamless transition from coarse scale meshes to fine scale meshes, we replace some elements consisting of the periodic part, in the vicinity of the nonperiodic part, by homogenized variable-node finite elements. To demonstrate the performance of the proposed method, several examples involving defects embedded in composite materials are given. It is shown that the proposed method have outstanding advantages over fully fine scale analysis in terms of computational costs without losing its accuracy.