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Local elasticity map and plasticity in a model Lennard-Jones glass

In this work we calculate the local elastic moduli in a weakly polydisperse 2DLennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse grained 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 scaffoldingand of soft zones. Only recently calculated in non homogeneous materials, the local elastic structure plays a crucial role in the elasto-plastic response of the amorphous material. For a small macroscopic shear strain the structures associated with the non-affine 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 form of plastic rearrangements. The spatio-temporal 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.