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We present a detailed mass reconstruction and a novel study on thesubstructure properties in the core of the CLASH and Frontier Fields galaxycluster MACS J0416.1-2403. We show and employ our extensive spectroscopic dataset taken with the VIMOS instrument as part of our CLASH-VLT program, toconfirm spectroscopically 10 strong lensing systems and to select a sample of175 plausible cluster members to a limiting stellar mass of log(M_*/M_Sun) ~8.6. We reproduce the measured positions of 30 multiple images with aremarkable median offset of only 0.3" by means of a comprehensive stronglensing model comprised of 2 cluster dark-matter halos, represented by coredelliptical pseudo-isothermal mass distributions, and the cluster membercomponents. The latter have total mass-to-light ratios increasing with thegalaxy HST/WFC3 near-IR (F160W) luminosities. The measurement of the totalenclosed mass within the Einstein radius is accurate to ~5%, includingsystematic uncertainties. We emphasize that the use of multiple-image systemswith spectroscopic redshifts and knowledge of cluster membership based onextensive spectroscopic information is key to constructing robusthigh-resolution mass maps. We also produce magnification maps over the centralarea that is covered with HST observations. We investigate the galaxycontribution, both in terms of total and stellar mass, to the total mass budgetof the cluster. When compared with the outcomes of cosmological $N$-bodysimulations, our results point to a lack of massive subhalos in the innerregions of simulated clusters with total masses similar to that of MACSJ0416.1-2403. Our findings of the location and shape of the cluster dark-matterhalo density profiles and on the cluster substructures provide intriguing testsof the assumed collisionless, cold nature of dark matter and of the role playedby baryons in the process of structure formation.

CLASH-VLT: Insights on the mass substructures in the Frontier Fields Cluster MACS J0416.1-2403 through accurate strong lens modeling