In this paper, several simulations involving the compaction and the shearing of mixtures of hard and soft grains are performed in 2D plane-strain conditions. The multibody meshfree numerical tool developed for this purpose is first presented, and the focus is then put on the influence of the proportions of rigid and deformable grains in the mixture on the mechanical response at large strains. Dedicated postprocessing techniques reveal a wide range of behaviors, both in terms of macroscopic response and in micromechanical phenomena. Broadly speaking, the strength and the dilatancy of the mixture decrease when the proportion of soft grains is increased. There are, however, interesting exceptions to this trend at very high and very low contents of soft grains, which are analyzed in dedicated sections. This preliminary work paves the way to more comprehensive studies of this class of materials, which is still hardly understood but presents some potential in a wide range of applications.