Context. Under cold conditions in dense cores, gas-phase molecules and atoms are depleted from the gas-phase to the surface of interstellar grains. Considering the time scales and physical conditions within these cores, a portion of these molecules has to be brought back into the gas-phase to explain their observation by milimeter telescopes.Aims. We tested the respective efficiencies of the different mechanisms commonly included in the models (photo-desorption, chemical desorption, and cosmic-ray-induced whole-grain heating). We also tested the addition of sputtering of ice grain mantles via a collision with cosmic rays in the electronic stopping power regime, leading to a localized thermal spike desorption that was measured in the laboratory.Methods. The ice sputtering induced by cosmic rays has been added to the Nautilus gas-grain model while the other processes were already present. Each of these processes were tested on a 1D physical structure determined by observations in TMC1 cold cores. We focused the discussion on the main ice components, simple molecules usually observed in cold cores (CO, CN, CS, SO, HCN, HC3N, and HCO+), and complex organic molecules (COMs such as CH3OH, CH3CHO, CH3OCH3, and HCOOCH3). The resulting 1D chemical structure was also compared to methanol gas-phase abundances observed in these cores.Results. We found that all species are not sensitive in the same way to the non-thermal desorption mechanisms, and the sensitivity also depends on the physical conditions. Thus, it is mandatory to include all of them. Chemical desorption seems to be essential in reproducing the observations for H densities smaller than 4 × 104 cm−3, whereas sputtering is essential above this density. The models are, however, systematically below the observed methanol abundances. A more efficient chemical desorption and a more efficient sputtering could better reproduce the observations.Conclusions. In conclusion, the sputtering of ices by cosmic-rays collisions may be the most efficient desorption mechanism at high density (a few 104 cm−3 under the conditions studied here) in cold cores, whereas chemical desorption is still required at smaller densities. Additional works are needed on both mechanisms to assess their efficiency with respect to the main ice composition.< Réduire