  We explain the Lorentz resonances in plasmonic crystals that consist of 2D
nano dielectric inclusions as the interaction between resonant material
properties and geometric resonances of electrostatic nature. One example of
such plasmonic crystals are graphene nanosheets that are periodically arranged
within a non-magnetic bulk dielectric. We identify local geometric resonances
on the length scale of the small scale period. From a materials perspective,
the graphene surface exhibits a dispersive surface conductance captured by the
Drude model. Together these phenomena conspire to generate Lorentz resonances
at frequencies controlled by the surface geometry and the surface conductance.
The Lorentz resonances found in the frequency response of the effective
dielectric tensor of the bulk metamaterial is shown to be given by an explicit
formula, in which material properties and geometric resonances are decoupled.
This formula is rigorous and obtained directly from corrector fields describing
local electrostatic fields inside the heterogeneous structure. Our analytical
findings can serve as an efficient computational tool to describe the general
frequency dependence of periodic optical devices. As a concrete example, we
investigate two prototypical geometries composed of nanotubes and nanoribbons.
