  Amorphous materials such as metallic, polymeric, and colloidal glasses,
exhibit complex preparation-dependent mechanical response to applied shear. We
perform numerical simulations to investigate the mechanical response of binary
Lennard-Jones glasses undergoing athermal, quasistatic pure shear as a function
of the cooling rate $R$ used to prepare them. The ensemble-averaged stress
versus strain curve $\langle\sigma(\gamma)\rangle$ resembles the spatial
average in the large size limit, which appears smooth and displays a putative
elastic regime at small strains, a yielding-related peak at intermediate
strain, and a plastic flow regime at large strains. In contrast, for each glass
configuration in the ensemble, the stress-strain curve consists of many short
nearly linear segments that are punctuated by particle-rearrangement-induced
rapid stress drops. We quantify the shape of the small stress-strain segments,
as well as the frequency and size of the stress drops in each glass
configuration. We decompose the stress loss into the loss from particle
rearrangements and from softening i.e., the reduction of the slopes of the
linear segments in $\sigma(\gamma)$), and then compare the two contributions as
a function of $R$ and $\gamma$. For the current studies, the
rearrangement-induced stress loss is larger than the softening-induced stress
loss, however, softening stress losses increase with decreasing cooling rate.
We also characterize the structure of the potential energy landscape along the
strain direction for glasses prepared with different $R$, and observe a
dramatic change of the properties of the landscape near the yielding
transition. We then show that the rearrangement-induced energy loss per strain
can serve as an order parameter for the yielding transition, which sharpens for
slow cooling rates and in the large system-size limit.
