A cantilevered piezoelectric bar meshed with solid elements. In the first load case,
the bar is subject to a sinusoidal electric potential at the free end. The applied
potential triggers a structural deformation in the material. In the second load
case, the output displacement from the previous load case is exported and added as
input enforced displacement. This triggers the same voltage response, thereby
demonstrating reverse piezoelectric effect.
Boundary Conditions
The boundary conditions defined in the model are as follows:
In load case 1, the sinusoidal voltage is scaled by an amplitude of 1000 kV
and applied at the dependent grid of the MPC.
In load case 2, enforced displacement (exported from load case 1) is applied
on the same MPC grid, to study the output voltage.
Figure 1. Boundary conditions used in the model
Material Properties
The material property definitions used in the model are as follows:
Anisotropic Dielectric matrix (MAT2PT)
Piezoelectric coupling matrix (MATPZO) – Strain charge
form
Orthotropic elasticity coefficients (MAT9OR)
E1
60.61 GPa
E2
48.31 GPa
E3
60.61 GPa
V12
0.512
V13
0.289
V23
0.512
G12=G23
23.0 GPa
G23
23.5 GPa
Results
Load case 1: Applied sinusoidal voltage
It can be noted that the applied
voltage triggers a structural deformation which is also sinusoidal.Figure 2. Results for load case 1
Load case 2: Reverse piezoelectric effect (applied displacement)
It can be
noted that the output electric potential (plotted at dependent grid of
MPC) is identical to the applied voltage in load case 1, thereby
demonstrating reverse piezoelectric effect.Figure 3. Results for load case 2