We present a new set of models for intermediate mass AGB stars (4.0, 5.0 and, 6.0 Msun) at different metallicities (-2.15<=Fe/H]<=+0.15). This integrates the existing set of models for low mass AGB stars (1.3<=M/M<=3.0) already included in the FRUITY database. We describe the physical and chemical evolution of the computed models from the Main Sequence up to the end of the AGB phase. Due to less efficient third dredge up episodes, models with large core masses show modest surface enhancements. The latter is due to the fact that the interpulse phases are short and, then, Thermal Pulses are weak. Moreover, the high temperature at the base of the convective envelope prevents it to deeply penetrate the radiative underlying layers. Depending on the initial stellar mass, the heavy elements nucleosynthesis is dominated by different neutron sources. In particular, the s-process distributions of the more massive models are dominated by the ean~reaction, which is efficiently activated during Thermal Pulses. At low metallicities, our models undergo hot bottom burning and hot third dredge up. We compare our theoretical final core masses to available white dwarf observations. Moreover, we quantify the weight that intermediate mass models have on the carbon stars luminosity function. Finally, we present the upgrade of the FRUITY web interface, now also including the physical quantities of the TP-AGB phase of all the models included in the database (ph-FRUITY).
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