  We investigate experimentally the mechanical response to shear of a 2D
packing of grains across the jamming transition. First, we develop a dedicated
experimental setup, together with tracking and photoelastic techniques in order
to prepare the packing in a controlled fashion and to quantify the stress and
strain tensors at the grain scale. Second, we install a inflating probe (a 2D
"balloon"), which shears the packing with a cylindrical symmetry. We probe
experimentally stresses and strains for strain amplitudes as low as $10^{-3}$
and for a range of packing fractions within $2\%$ variation around the jamming
transition. We observe not only that shear strain induces shear stresses, but
also normal stresses. Moreover, we show that both shear and normal stresses
behave nonlinearly with the shear strain. Finally, we show by scaling analysis
that the constitutive laws are controlled by the Jamming transition.
