Concurrent multiscale analysis without meshing: Microscale representation with CutFEM and micro/macro model blending

In this paper, we develop a novel unfitted multiscale framework that combines two separate scales represented by only one single computational mesh. Our framework relies on a mixed zooming technique where we zoom at regions of interest to capture microscale properties and then mix the micro and macroscale properties in a transition region. Furthermore, we use homogenization techniques to derive macro model material properties. The microscale features are discretized using CutFEM. The transition region between the micro and macroscale is represented by a smooth blending function. To address the issues with ill-conditioning of the multiscale system matrix due to the arbitrary intersections in cut elements and the transition region, we add stabilization terms acting on the jumps of the normal gradient (ghost-penalty stabilization). We show that our multiscale framework is stable and is capable to reproduce mechanical responses for heterogeneous structures in a mesh-independent manner. The efficiency of our methodology is exemplified by 2D and 3D numerical simulations of linear elasticity problems.