Embedded Strong Discontinuity Model Based Multiscale Finite Element Method for Strain Localization Analysis

Strain localization is a common factor that may lead to the failure of solid structure and its numerical analysis becomes an important aspect for the structural safety evaluation. Due to the heterogeneity and multiscale nature, however, traditional numerical methods need to resolve the structure at the fine scale to obtain reasonable results, which increases drastically the computational scale and cost. To solve this problem, an embedded strong discontinuity model based multiscale finite element method is proposed here. In this method, both coarse and fine scale elements are used to represent the structure. The embedded strong discontinuity model is first introduced into the fine element to describe the discontinuity and the corresponding additional displacement jump degree of freedom on the elemental level can be eliminated with the condensation technique, which keeps the dimensions of the stiffness matrix unchanged. Then, an enhanced multi-node coarse element technique is proposed, which can adaptively insert coarse nodes according to the intersection between the discontinuity line and coarse element boundary and thus guarantees the proper transformation of information between the fine and coarse elements. The problem can then be effectively solved on the coarse scale level. Moreover, a solution decomposition technique, in which the fine scale solution is decomposed into the downscaling and local perturbation solutions, is adopted to eliminate the unbalance forces within the unit cell in the elasto-plastic analysis. Finally, two representative examples are presented to demonstrate the accuracy and effectiveness of the proposed method through the comparisons with the results of the embedded finite element method. © 2017, Editorial Office of Chinese Journal of Theoretical and Applied Mechanics. All right reserved.