ASTROPHYSICAL SHOCKS ARE KNOWN TO BE PROMINENT SOURCES OF NON-THERMAL PARTICLES AND EMISSION. IN PARTICULAR STRONG SHOCKS AT SUPERNOVA REMNANT BLAST WAVES ARE THOUGHT TO ACCELERATE GALACTIC COSMIC RAYS (CRS) UP TO ABOUT 10^17EV VIA DIFFUSIVE SHOCK ACCELERATION (DSA). THE CHEMICAL COMPOSITION OF GALACTIC CRS NOW MEASURED WITH GREAT ACCURACY BY PAYLOADS AND SATELLITES IS REMINISCENT OF THAT OF THE TYPICAL INTERSTELLAR MEDIUM ALTHOUGH WITH SOME SIGNIFICANT DEVIATIONS. OBSERVATIONS REVEAL: 1) AN ELECTRON/PROTON RATIO OF ABOUT 1% AT ABOUT 10 GEV (2) A GENERAL ENHANCEMENT OF THE REFRACTORY ELEMENTS RELATIVE TO THE VOLATILE ONES (3) AMONG THE VOLATILE ELEMENTS AN ENHANCEMENT OF THE HEAVIER ELEMENTS RELATIVE TO THE LIGHTER ONES AND (4) A DISCREPANT HARDENING OF CR NUCLEI HEAVIER THAN HYDROGEN. SUCH PECULIAR TRENDS CONTAIN PRECIOUS INFORMATION ABOUT THE DEPENDENCE OF THE ACCELERATION PROCESS ON THE PARTICLE MASS/CHARGE RATIO A TREND THAT HAS NO THEORETICAL COUNTERPART IN THE DSA THEORY YET.BUILDING ON OUR RECENT SUCCESSES IN MODELING ELECTRON AND PROTON DSA AT NON-RELATIVISTIC ASTROPHYSICAL SHOCKS VIA FIRST-PRINCIPLES KINETIC SIMULATIONS WE WILL PERFORM MULTI-SPECIES PARTICLE-IN-CELLS SIMULATIONS OF SUCH SYSTEMS ALSO INCLUDING NUCLEI HEAVIER THAN HYDROGEN IN ORDER TO INVESTIGATE THERMALIZATION INJECTION AND ACCELERATION OF SPECIES WITH DIFFERENT MASS/CHARGE RATIO.WE WILL ALSO ANALYZE HOW THE SIMULATION OUTPUTS COMPARE WITH THE OBSERVED CR ABUNDANCES IN ORDER TO BUILD A MODEL FOR DSA THAT ACCOUNTS FOR THE RELATIVE ACCELERATION EFFICIENCY OF ENERGETIC ELECTRONS PROTONS AND HEAVIER IONS.FINALLY WE WILL ASSESS THE POSSIBLE CONTRIBUTION OF ACCELERATED HEAVY IONS ESPECIALLY HELIUM TO THE GENERATION OF MAGNETIC TURBULENCE VIA CR-DRIVEN INSTABILITIES -CRUCIAL TO FOSTER RAPID PARTICLE ENERGIZATION- AND TO THE HADRONIC GAMMA-RAY EMISSION FROM YOUNG SUPERNOVA REMNANTS.