We present a new set of models for intermediate mass AGB stars ( 4.0 , 5.0 and , 6.0 M _ { \odot } ) at different metallicities ( -2.15 \leq [ Fe/H ] \leq +0.15 ) .
This integrates the existing set of models for low mass AGB stars ( 1.3 \leq M/M _ { \odot } \leq 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 ^ { 22 } Ne ( \alpha , n ) ^ { 25 } Mg 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 ) .