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An extended and complete thermodynamical model of third-order electro-elastic coupling is proposed with symmetry analyses and density functional theory (DFT) calculations to evaluate consistently the various linear and non-linear coefficients. It is shown that in non-centrosymmetric materials, electrostrictive and non-linear piezoelectric phenomena are strongly coupled, except for materials crystallizing in a cubic lattice associated to the 432 point group. Thorough numerical results are given for GaN and AlN compounds in the Würtzite structure. Electrostriction dominates, but non-linear elasticity and non-linear piezoelectricity must be taken into account for strain evaluation whereas non-linear piezoelectricity yields a significant correction for electric field.