The original 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 temperatures up to the glass transition. We propose to extend the theory in the direction of 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. As a reference, we compare our theoretical results obtained in this way to those obtained from athermal quasistatic simulations (AQS).
As expected, the VDOS of the minimized states does not show signatures of the deformation. In contrast, the VDOS evaluated using (γINM) protocol changes significantly, which indicates that the γINMs can effectively describe the effect of deformation on the vibrational spectrum, in the same as the standard INMs effectively describe the effect of temperature on the VDOS. Moreover, 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 of the γINM in different deformed states and use it to reconstruct the stress-strain curve. Our choice of (γINM) gives good results, predicting both deviation from linear regime at ≈ 5% deformation and a significant drop of the stress around 10%, which is the typical strain where the yielding occurs.
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. This framework also provides a unifying description of strain-induced and thermal-induced softening of glassy materials.