  We explore the nonlinear variational modelling of two-dimensional (2D)
crystal plasticity based on strain energies which are invariant under the full
symmetry group of 2D lattices. We use a natural parameterization of strain
space via the upper complex Poincar\'e half-plane. This transparently displays
the constraints imposed by lattice symmetry on the energy landscape.
Quasi-static energy minimization naturally induces bursty plastic flow and
shape change in the crystal due to the underlying coordinated basin-hopping
local strain activity. This is mediated by the nucleation, interaction, and
annihilation of lattice defects occurring with no need for auxiliary
hypotheses. Numerical simulations highlight the marked effect of symmetry on
all these processes. The kinematical atlas induced by symmetry on strain space
elucidates how the arrangement of the energy extremals and the possible
bifurcations of the strain-jump paths affect the plastification mechanisms and
defect-pattern complexity in the lattice.
