We analyze the effect of particle shape non-convexity on the quasi-static behavior of granular materials by means of contact dynamics simulations. The particles are regular aggregates of four overlapping spheres described by a nonconvexity parameter depending on the relative positions of the particles. Several packings are first submitted to isotropic compression without friction. We find that, as in 2D, the solid fraction of isotropic packings increases with non-convexity up to a maximum value and then declines to be nearly equal to that of a packing composed of only spheres. It is also remarkable that the coordination number increases quickly and saturates so that the packings composed of grains with a high level of nonconvexity are looser but more strongly connected. Then, the quasi-static behavior, structural and force anisotropies are analyzed by subjecting each packing to a triaxial compression. We find that the shear strength increases with non-convexity. We show that this increase results from the presence of multiple contacts between trimers leading to enhanced frictional interlocking.