Piezoelectricity Free Material Optimization Results Summary Free Material Optimization of Piezoelectric Material Fabian Wein 1 , M. Stingl 1 WCSMO-10 Mai 19-24, 2013 1 Applied Mathematics, University Erlangen-Nuremberg, Germany Fabian Wein Free Material Optimization of Piezoelectric Material
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Free Material Optimization of Piezoelectric Material
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Piezoelectricity Free Material Optimization Results Summary
Free Material Optimization of Piezoelectric Material
Fabian Wein1, M. Stingl1
WCSMO-10Mai 19-24, 2013
1 Applied Mathematics, University Erlangen-Nuremberg, Germany
Fabian Wein Free Material Optimization of Piezoelectric Material
Piezoelectricity Free Material Optimization Results Summary
Piezoelectric Material: Overview
main property: convert electric energy ↔ mechanic energy
sinter sputter electrodes polarize
P P
electrodes
2D model electric excitation
standard assumption: homogeneous material with uniform polarizationFabian Wein Free Material Optimization of Piezoelectric Material
Piezoelectricity Free Material Optimization Results Summary
Piezoelectric Polarization
base cell
electric neutral above temperature TC
dipole moment and deformation below TC
explains mechanical ↔ electric coupling
macroscopic view
randomly orientated domains (clusters)
electric neutral isotropic material
polarization
uniform alignment of domains
electric dipole moment
transversal isotropic (= orthotropic in 2D)
a) T > T
Pb ZrO
−+
2+ 4+2−
3
cb) T < T
c
PZT cell
domains; wikipedia
Fabian Wein Free Material Optimization of Piezoelectric Material
Piezoelectricity Free Material Optimization Results Summary
Static Linear Piezoelectric Phenomenologic Continuum Model
constitutive equations and coupled FEM
σ = [c ]S− [e ]>E
D = [e ]S+ [ε]E→
(Kuu Kuφ
K>uφ−Kφφ
)(uφ
)=
(f0
)
mechanic stress σ, strain S, electric displacement D, electric field E