In this paper, we propose a robust concurrent multiscale method for
continuum-continuum coupling based on the cut finite element method. The
computational domain is defined in a fully non-conforming fashion by
approximate signed distance functions over a fixed background grid and
decomposed into microscale and macroscale regions by a novel zooming technique.
The zoom interface is represented by a signed distance function which is
allowed to intersect the computational mesh arbitrarily. We refine the mesh
inside the zooming region hierarchically for high-resolution computations. In
the examples considered here, the microstructure can possess void, and hard
inclusions and the corresponding geometry is defined by a signed distance
function interpolated over the refined mesh. In our zooming technique, the
zooming interface is allowed to intersect the microstructure interface in a
arbitrary way. Then, the coupling between the subdomains is applied using
Nitsche's method across interfaces. This multiresolution framework proposes an
efficient stabilized algorithm to ensure the stability of elements cut by the
zooming and the microstructure interfaces. It is tested for several multiscale
examples to demonstrate its robustness and efficiency for elasticity and
plasticity problems