Multiscale modeling of linear elastic heterogeneous structures based on a localized model order reduction approach

In analyzing large scale structures it is necessary to take into account the fine scale heterogeneity for accurate failure prediction. Resolving fine scale features in the numerical model drastically increases the number of degrees of freedom, thus making full fine-scale simulations infeasible, especially in cases where the model needs to be evaluated many times. In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. Addressing applications where the assumption of scale separation does not hold, the influence of the fine scale on the coarse scale is modelled directly by the use of an additive split of the displacement field. Possible coarse and fine scale solutions are exploited for a representative volume element (RVE) to construct local approximation spaces. The local spaces are designed such that local contributions of RVE subdomains can be coupled in a conforming way. Therefore, the resulting global system of equations takes the effect of the fine scale on the coarse scale into account, is sparse and reduced in size compared to the full order model. Several numerical experiments show the accuracy and efficiency of the method.