Higher order effects in ferroelectric materials are investigated by integrating electron density calculations using quantum mechanics into a homogenized, nonlinear continuum modeling framework. Electrostatic stresses based on the Hellmann-Feynman theorem are used to identify connections with the higher order quadrupole density. These higher order relations are integrated into a nonlinear mechanics free energy function to simulate electromechanical coupling. A specific example is investigated by conducting density functional theory (DFT) calculations on barium titanate and fitting the results to a thermodynamic potential function. Through the use of nonlinear geometric effects, electromechanical coupling is obtained without the use of electrostrictive or piezoelectric coupling coefficients.

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