  The jamming transition, generally manifested by a rapid increase of rigidity
under compression (i.e., compression hardening), is ubiquitous in amorphous
materials. Here we study shear hardening in deeply annealed frictionless
packings generated by numerical simulations, reporting critical scalings absent
in compression hardening. We demonstrate that hardening is a natural
consequence of shear-induced memory destruction. Based on an elasticity theory,
we reveal two independent microscopic origins of shear hardening: (i) the
increase of the interaction bond number and (ii) the emergence of anisotropy
and long-range correlations in the orientations of bonds, the latter highlights
the essential difference between compression and shear hardening. Through the
establishment of physical laws specific to anisotropy, our work completes the
criticality and universality of jamming transition, and the elasticity theory
of amorphous solids.
