  This is the second paper (the first was astro-ph/9704267) of a series
analysing the Galactic Cosmic Ray (GCR) composition and origin. In this we
present a quantitative model of GCR origin and acceleration based on the
acceleration of a mixture of interstellar and/or circumstellar gas and dust by
supernova remnant blast waves. We present results from a nonlinear shock model
which includes (i) the direct acceleration of interstellar gas-phase ions, (ii)
a simplified model for the direct acceleration of weakly charged dust grains to
energies of order 100keV/amu simultaneously with the gas ions, (iii) frictional
energy losses of the grains colliding with the gas, (iv) sputtering of ions of
refractory elements from the accelerated grains and (v) the further shock
acceleration of the sputtered ions to cosmic ray energies. The calculated GCR
composition and spectra are in good agreement with observations.
