  We analyze the isotropic compaction of mixtures composed of rigid and
deformable incompressible particles by the non-smooth contact dynamics approach
(NSCD). The deformable bodies are simulated using a hyper-elastic neo-Hookean
constitutive law by means of classical finite elements. For mixtures that
varied from totally rigid to totally deformable particles, we characterize the
evolution of the packing fraction, the elastic modulus, and the connectivity as
a function of the applied stresses when varying inter-particle coefficient of
friction. We show first that the packing fraction increases and tends
asymptotically to a maximum value $\phi_{max}$, which depends on both the
mixture ratio and the inter-particle friction. The bulk modulus is also shown
to increase with the packing fraction and to diverges as it approaches
$\phi_{max}$. From the micro-mechanical expression of the granular stress
tensor, we develop a model to describe the compaction behavior as a function of
the applied pressure, the Young modulus of the deformable particles, and the
mixture ratio. A bulk equation is also derived from the compaction equation.
This model lays on the characterization of a single deformable particle under
compression together with a power-law relation between connectivity and packing
fraction. This compaction model, set by well-defined physical quantities,
results in outstanding predictions from the jamming point up to very high
densities and allows us to give a direct prediction of $\phi_{max}$ as a
function of both the mixture ratio and the friction coefficient.
