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
