  The nonthermal source abundances of elements play a crucial role in the
understanding of cosmic ray (CR) phenomena from a few GeV up to several tens of
EeV. We present a first systematic approach to describe the change of the
abundances from the thermal to the nonthermal state via diffusive shock
acceleration by a temporally evolving shock. We consider hereby not only
ionization states of elements contained in the ambient gas, which we allow to
be time dependent due to shock heating, but also elements condensed on solid,
charged dust grains which can be injected into the acceleration process as
well. Our generic parametrized model is then applied to the case of particle
acceleration by supernova remnants in various ISM phases, for which we use
state-of-the-art computation packages to calculate the ionization states of all
elements. The resulting predictions for low energy cosmic ray (LECR) source
abundances are compared with the data obtained by various experiments.
  We obtain excellent agreement for shocks in warm ionized ISM environments,
which include HII regions, if dust grains are injected into the diffusive shock
acceleration process with a much higher efficiency than ions. Less dependence
of the fit quality is found on the mass-to-charge ratio of ions. For neutral
environments, assuming that there are shocks in the weakly ionized component,
and for the hot ionized medium we obtain generally inferior fits, but except
for the cold neutral medium we do not exclude them as subdominant sites of
Galactic CR production. The key challenge is found to be putting the LECR
abundance of pure gas phase elements like neon and the (semi-)volatile elements
phosphorus, sulfur and chlorine into the right balance with silicon, calcium
and elements of the iron group. Finally, a brief outlook to the potential
consequences for the understanding of the CR composition at higher energies is
presented.
