  We describe a phase transition that gives rise to structurally non-trivial
states in a two-dimensional ordered network of particles connected by harmonic
bonds. Monte Carlo simulations reveal that the network supports, apart from the
homogeneous phase, a number of heterogeneous "pleated" phases, which can be
stabilised by an external field. This field is conjugate to a global collective
variable quantifying "non-affineness", i.e.~the deviation of local particle
displacements from local affine deformation. In the pleated phase, stress is
localised in ordered rows of pleats and eliminated from the rest of the
lattice. The {\em kinetics} of the phase transition is unobservably slow in
molecular dynamics simulation near coexistence, due to very large free energy
barriers. When the external field is increased further to lower these barriers,
the network exhibits rich dynamic behaviour: it transforms into a {\em
metastable} phase with the stress now localised in a {\em disordered}
arrangement of pleats. The pattern of pleats shows ageing dynamics and slow
relaxation to equilibrium. Our predictions may be checked by experiments on
tethered colloidal solids in dynamic laser traps.
