  In engineering crystal plasticity inelastic mechanisms correspond to
tensorial zero-energy valleys in the space of macroscopic strains. The flat
nature of such valleys is in contradiction with the fact that plastic slips,
mimicking lattice-invariant shears, are inherently discrete. A reconciliation
has recently been achieved in the mesoscopic tensorial model (MTM) of crystal
plasticity, which introduces periodically modulated energy valleys while also
capturing in a geometrically exact way the crystallographically-specific
aspects of plastic slips. In this paper, we extend the MTM framework, which in
its original form had the appearance of a discretized nonlinear elasticity
theory, by explicitly introducing the concept of plastic deformation. The
ensuing model contains a novel matrix-valued spin variable, representing the
quantized plastic distortion, whose rate-independent evolution can be described
by a discrete (quasi-)automaton. The proposed reformulation of the MTM leads to
a considerable computational speedup associated with the use of a robust and
efficient hybrid Gauss-Newton--Cauchy energy minimization algorithm. To
illustrate the effectiveness of the new approach, we present a detailed
case-study focusing on the aspects of crystal plasticity that are beyond reach
for the classical continuum theory. Thus, we provide compelling evidence that
the re-formulated MTM is fully adequate to deal with the intermittency of
plastic response under quasi-static loading. In particular, our numerical
experiments show that the statistics of dislocational avalanches, associated
with plastic yield in 2D square crystals, exhibits a power-law tail with a
critical exponent matching the value predicted by general theoretical
considerations and also independently observed in discrete-dislocation-dynamics
(DDD) simulations.
