  We study theoretically the dynamics of soft glassy materials during the
process of stress relaxation following the rapid imposition of a shear strain.
By detailed numerical simulations of a mesoscopic soft glassy rheology model
and three different simplified continuum fluidity models, we show that a
dramatic shear localisation instability arises, in which the strain field
suddenly becomes heterogeneous within the sample, accompanied by a precipitous
drop in the stress. Remarkably, this instability can arise at extremely long
delay times after the strain was applied, due to the long-term memory inherent
to glassy systems. The finding that a catastrophic mechanical instability can
arise long after any deformation could have far reaching consequences for
material processing and performance, and potentially also for delayed
geophysical phenomena.
