In this work we first report on a theoretical model which provides the gate voltage dependence of the piezoelectric polarization charge in GaN HEMT devices. The model utilizes a generalization of Gauss' law, imposing constraints on the electric displacement vector D. The constraint on D is given by the continuity of the perpendicular component of the displacement vector across an interface. Poisson's equation is then solved across various layers under proper boundary conditions for the applied bias. The piezoelectric polarization charge is reduced due to the electromechanical coupling compared to the uncoupled case. Under high sheet electron densities, the correction in the piezoelectric polarization charge is also lower due to smaller electric fields. The theoretical model is then incorporated in the particle-based device simulator and device transfer and output characteristics are calculated without and with the bias dependent polarization charge. We find that percentage change in drain current increases with larger negative bias on the gate, due to the larger vertical electric fields.