  Changes in the mechanical properties of granular materials, induced by
variations in the intrinsic compressibility of the particles, are investigated
by means of numerical simulations based on the combination of the Finite
Element and Contact Dynamics methods. Assemblies of athermal 2D particles are
subjected to quasi-static uni-axial compactions up to packing fractions close
to $1$. Inspired by the contact mechanics in the Hertz's limit, we show that
the effect of the compressibility of the particles both on the global and the
local stresses, can be described by considering only the packing fraction of
the system. This result, demonstrated in the whole range of accessible packing
fractions in case of frictionless particles, remains relevant for moderate
inter-particles coefficients of friction. The small discrepancies observed with
frictional particles originate from irreversible local reorganizations in the
system, the later being facilitated by the compressibility of the particles.
