  We present a numerical study of the mechanical response of a 2D Lennard-Jones
amorphous solid under steady quasistatic and athermal shear. We focus here on
the evolution of local stress components. While the local stress is usually
taken as an order parameter in the description of the rheological behaviour of
complex fluids, and for plasticity in glasses, we show here that the knowledge
of local stresses is not sufficient for a complete description of the plastic
behaviour of our system. The distribution of local stresses can be
approximately described as resulting from the sum of localized quadrupolar
events with an exponential distribution of amplitudes. However, we show that
the position of the center of the quadrupoles is not related to any special
evolution of the local stress, but must be described by another variable.
