An Effective Third-Order elastic tensor for strain-induced changes in second-order elastic coefficients

Ab initio calculations of third-order elastic coefficients

This study reviews the thermodynamic definition of the third-order elastic
tensor and proposes using an"effective"third-order elastic tensor.We extend the ab initio approach to calculate third-order elastic tensors under finite pressure and apply it to two cubic systems, namely, nacl and mgo.As applications and validations, we evaluate (a) strain-induced changes in second-order elastic coefficients and (b) pressure derivatives of second-order elastic coefficients based on ab initio calculations.Good agreement between third-order elasticity-based predictions and numerically calculated values confirms the validity of our theory.