  We derive the electromagnetic medium equivalent to a collection of
all-dielectric nano-particles (enjoying high refractive indices) distributed
locally non-periodically in a smooth domain $\Omega$. Such distributions are
used to model well known structures in material sciences as the Van-der-Waals
heterostructures. Since the nano-particles are all-dielectric, then the
permittivity remains unchanged while the permeability is altered by this
effective medium. This equivalent medium describes, in particular, the
effective medium of 2 dimensional type Van-der-Waals heterostructures. These
structures are 3 dimensional which are build as superposition of identical
(2D)-sheets each supporting locally non-periodic distributions of
nano-particles. An explicit form of this effective medium is provided for the
particular case of honeycomb heterostructures.
  At the mathematical analysis level, we propose a new approach to derive the
effective medium when the subwavelength nano-particles are distributed
non-periodically. The first step consists in deriving the point interaction
approximation, also called the Foldy-Lax approximation. The scattered field is
given as a superposition of dipoles (or poles for other models) multiplied by
the elements of a vector which is itself solution of an algebraic system. This
step is done regardless of the way how the particles are distributed. As a
second step, which is the new and critical step, we rewrite this algebraic
system according to the way how these nano-particles are locally distributed.
The new algebraic system will then fix the related continuous Lippmann
Schwinger system which, in its turn, indicates naturally the equivalent medium.
