Prediction of amorphous plasticity based on nonaffine lattice dynamics

The nonaffine lattice dynamics framework was developed only for small deformations and T=0. The introduction of the instantaneous normal modes (INM) extended the theory to finite T. We propose to extend the theory to large deformations by constructing the INM of deformed states (γINM) using the instantaneous Affine Transform (AT) from the non-deformed state (γ = 0) to the deformed state as a proxy for non-equilibrated protocol that generates the γINMs. We compare our theoretical results to those obtained from athermal quasistatic simulations (AQS). The increase of γ has a similar effect on VDOS of γINM as the increase of the temperature on the INM, thus leading to a similar softening of the material. To directly test if the softening occurs, we calculate the shear modulus and use it to reconstruct the stress-strain, which for our choice of (γINM) shows a significant drop of the stress around 10% deformation, in agreement with AQS.
This may open up the possibility to provide predictions of stress-strain behaviour and yielding using only snapshots of underformed samples as input, since the construction of γINM is a purely analytical procedure.