  This paper analyzes the compaction behavior of assemblies composed of soft
(elastic) spherical particles beyond the jammed state, using three-dimensional
non-smooth contact dynamic simulations. The assemblies of particles are
characterized using the evolution of the packing fraction, the coordination
number, and the von Misses stress distribution within the particles as the
confining stress increases. The packing fraction increases and tends toward a
maximum value close to $1$, and the mean coordination number increases as a
square root of the packing fraction. As the confining stress increases, a
transition is observed from a granular-like material with exponential tails of
the shear stress distributions to a continuous-like material characterized by
Gaussian-like distributions of the shear stresses. We develop an equation that
describes the evolution of the packing fraction as a function of the applied
pressure. This equation, based on the micromechanical expression of the
granular stress tensor, the limit of the Hertz contact law for small
deformation, and the power-law relation between the packing fraction and the
coordination of the particles, provides good predictions from the jamming point
up to very high densities without the need of tuning any parameters.
