  In this paper, we present a robust and efficient unfitted concurrent
multiscale method for continuum-continuum coupling, based on the Cut Finite
Element Method (CutFEM). The computational domain is defined using approximate
signed distance functions over a fixed background mesh and is decomposed into
microscale and macroscale regions using a novel zooming technique. The zoom
interface is represented by a signed distance function intersecting the
computational mesh arbitrarily. The mesh inside the zoomed region is
hierarchically refined to resolve the microstructure. In the examples
considered, the microstructure may contain voids and hard inclusions, and its
geometry is defined implicitly by a signed distance function interpolated over
the refined mesh.
  Our zooming technique allows the zoom interface to intersect the
microstructure interface in an arbitrary fashion, enabling greater flexibility
and accuracy in the modelling of complex geometries. The micro and macro
regions are coupled using Nitsche's method, ensuring stability and accuracy in
the solution. Ghost penalty terms are utilised to ensure the stability of cut
elements along the zoom interface and the microstructure interface.
  To demonstrate the effectiveness of our framework, we apply it for modelling
several heterogeneous structures with both linear elasticity and plasticity
constitutive behaviours. The results show that our framework is robust and
efficient, producing accurate and reliable solutions for such problems. Our
proposed method provides a highly versatile and effective approach to
multiscale modeling of structures with complex microstructures, and has the
potential to be extended to problems requiring seamless moving of zooming
region(s) during the simulation, such as damage growth and fracture
propagation.
