  Using a numerical approach based on the coupling of the discrete and finite
element methods, we explore the variation of the bulk modulus K of soft
particle assemblies undergoing isotropic compression. As the assemblies densify
under pressure-controlled boundary conditions, we show that the non-linearities
of K rapidly deviate from predictions standing on a small-strain framework or
the Equivalent Medium Theory (EMT). Using the granular stress tensor and
extracting the bulk properties of single representative grains under
compression, we propose a model to predict the evolution of K as a function of
the sample's solid fraction and a reference state as the applied pressure P
tends to zero. The model closely reproduces the trends observed in our
numerical experiments confirming the behavior scalability of soft particle
assemblies from the individual particle scale. Finally, we present the effect
of the interparticle friction on K's evolution and how our model easily adapts
to such a mechanical constraint.
