A symmetry-based thermodynamical model of third-order electro-elastic coupling is applied to zinc-blende semiconductors. Density functional theory is used to calculate the complete set of linear and non-linear coefficients. The entanglement of non-linear piezoelectricity, electrostriction and other non-linear phenomena, is studied in details at the same level of theory. Numerical results for InxGa1−xP/GaP  quantum wells show the predominance of the non-linear piezoelectricity contribution. However, for a coupled non-linear model, the electrostriction has also to be taken into account. Finally, the non-linear elasticity gives a significant correction on the strain calculation.