Conventional Cone Penetration Tests (CPT) provide only strength parameters of soils, required to design geotechnical structures against failure. As these structures must furthermore be designed against operational loss of serviceability (excessive settlements of foundations for instance), deformability parameters of soils are then needed. Their characterization, using CPT –not correlations- is a problem that many researchers, from (Faugeras and al., 1983) to (Teyssier and al., 2021), have addressed over the last decades. This paper presents an investigation of the question, through a CPT-based test, adopting a numerical approach using the Discrete Element Method (DEM). As the real experiment, the simulation is carried out in a (virtual) calibration chamber with a penetrometer with a movable tip. The penetrometer is first monotonically driven into the soil until a depth of interest is reached; the tip is then monotonically unloaded, down to a small fraction of the tip resistance recorded at this depth. Thence, force-controlled cycles are imposed on the tip with a gradual increase of the force magnitude over time. The main results reveal very small irreversible displacements of the tip over the cycles whose amplitudes span a region of low fractions of the tip resistance, which is subsequently assimilated to a pseudo-elastic domain. The slopes of the force-displacement curve in this pseudo-elastic region barely differ from each other, which can be interpreted as a very small, if any, degradation of the soil deformation modulus. Then, there is a cycle from which these plastic displacement increments begin to be substantial; a significant decrement in the secant slope of the force-displacement curve is observed alongside the development of significant displacements of the tip. Such a test then allows to address the problems of the determination of both a soil deformation modulus (in the pseudo-elastic region of the curve) and a threshold stress that engenders important plastic deformations in it.