A multiscale finite element method with embedded strong discontinuity model for the simulation of cohesive cracks in solids

A multiscale finite element method with the embedded strong discontinuity model is proposed to simulate the cohesive cracks in solids. In the proposed method, the kinematic descriptions of the strong discontinuity and space discretization are considered based on the fine-scale with the strong discontinuity approach. Then, in order to correctly and conveniently deliver the discontinuous information between the coarse-scale and fine-scale, an enhanced coarse element strategy is proposed to construct the multiscale base functions that can well capture the discontinuous characteristics and preserve an adequate accuracy for the unit cells exhibiting a strong discontinuity. The main idea is that the coarse nodes of the enhanced coarse element can be dynamically added according to the identification of the intersection between the crack path and the boundaries of the unit cell during the computational procedure. The strategy overcomes the deficiency that the traditional coarse elements in the multiscale finite element method cannot well characterize the displacement jump property on the boundary of the unit cell. Moreover, to accurately obtain the microscopic displacement, the displacement decomposition technique is adopted to modify the downscale computations by adding the perturbation solutions. Numerical examples of normal tension and bending tests are presented to validate the proposed method by comparing the results with the analytical or fine finite element solutions. Finally, the three-point bending and four-point bending benchmarks are performed to further demonstrate the effectiveness and high efficiency of the method.