  We present a novel formalism to characterize elastic heterogeneities in
amorphous solids. In particular, we derive high-order strain-energy expansions
for pairwise energies under athermal quasistatic dynamics. We then use the
presented formalism to study the statistical properties of pairwise expansion
coefficients and their link with the statistics of soft, quasilocalized modes,
for a wide range of formation histories in both two- and three-dimensional
systems. We further exploit the presented framework to access local yield
stress maps by performing a non-linear stress-strain expansion within a cavity
embedded in a frozen matrix. We show that our "bond micromechanics" compare
well with the original "frozen matrix" method, with the caveat of
overestimating large stress activations. We additionally show how local yield
rules can be used as input for a scalar elasto-plastic model (EPM) to predict
the stress response of materials ranging from ductile to brittle. Finally, we
highlight some of the limits of simple mesoscale models in capturing the aging
dynamics of post-yielding systems. Intriguingly, we observe subdiffusive and
diffusive shearband growths for particle-based simulations and EPMs,
respectively.
