  This work presents a new modeling approach to macroscopic, polycrystalline
elasto-plasticity starting from first principles and a few well-defined
structural assumptions, incorporating the mildly rate-dependent (viscous)
nature of plastic flow and the microscopic origins of plastic deformations. For
the global dynamics, we start from a two-stage time-stepping scheme, expressing
the fact that in most real materials plastic flow is much slower than elastic
deformations, and then perform a detailed analysis of the slow-loading limit
passage. In this limit, a rate-independent evolution can be expected, but this
brings with it the possibility of jumps (relative to the "slow" time).
Traditionally, the dynamics on the jump transients often remain unspecified,
which leads to ambiguity and deficiencies in the energy balance. In order to
remedy this, the present approach precisely describes the energetics on the
jump transients as the limit of the rate-dependent evolutions at "singular
points". It turns out that rate-dependent behavior may (but does not have to)
prevail on the jump transients. Based on this, we introduce the new solution
concept of "two-speed solutions" to the elasto-plastic evolutionary system,
which incorporates a "slow" and a "fast" time scale, the latter of which
parametrizes the jump transients.
