A generalized multiscale independent cover method for nonlocal damage simulation

In this paper, a generalized multiscale independent cover method (MsICM) for nonlocal damage simulation is proposed. The independent cover approximation is used in the micro-scale elements and regular macro-scale elements. Mappings between different scales are derived by imposing essential boundary conditions in the fine scale and are updated continuously with the evolution of nonlocal damage of material points. The obtained multiscale basis function and adopted subdivision for two-level meshes lay a foundation for damage propagation across the boundary of macro-scale elements, which is a prominent feature of this approach. An adaptive multiscale scheme is used to further reduce the computational cost by setting a threshold of nonlocal equivalent strain in regular macro-scale elements for entering multiscale analysis. The independent cover method has merits of conveniently adding/deleting degrees of freedom (DOFs) of independent covers and performing unified continuum/discontinuum analysis by using the fictitious thin layer technique, which facilitates the natural transformation between macro and micro DOFs in damaged regions for MsICM in a concise way. In MsICM, the number of DOFs for solving the global equilibrium equation and the demand for computer memory are greatly reduced. Numerical examples demonstrate the correctness and effectiveness of the present technique for localization problems.