Look at the PhD viva...In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones
glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarsegrained
microscopic expressions for the strain, displacement, and stress fields. This method allows us to
calculate the local elasticity tensor and to quantify the deviation from linear elasticity local Hooke’s law at
different coarse-graining scales. From the results a clear picture emerges of an amorphous material with
strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke’s law at scales larger than
a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a
composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous
materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous
material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field
appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear
strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements.
The spatiotemporal evolution of this local elasticity map and its connection with long term
dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this
local parameter as a predictor of subsequent local plastic activity is also discussed.