  In recent work it was clarified that amorphous solids under strain control do
not possess nonlinear elastic theory in the sense that the shear modulus exists
but nonlinear moduli exhibit sample to sample fluctuations that grow without
bound with the system size. More relevant however for experiments are the
conditions of stress control. In the present Communication we show that also
under stress control the shear modulus exists but higher order moduli show
unbounded sample to sample fluctuation. The unavoidable consequence is that the
characterization of stress-strain curves in experiments should be done with a
stress-dependent shear modulus rather than with nonlinear expansions.
