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Qingwei Lau, PhD candidate
School of ME, SJTU
A FEM Study of displacement sensor based on
L-L Magnetostrictive/Piezoelectric block
magnetoelectric composite material
Excerpt from the Proceedings of the 2016 COMSOL Conference in Shanghai
Contents
1 Introduction
2 Modelling of ME effect
3 Implementation with COMSOL
4 Simulation
5 Results
▪ Magnetoelectric effect (ME) is the phenomenon of inducing magnetic
(electric) polarization by applying an external electric (magnetic) field.
Introduction
Single Phase
MaterialCr2O3
Composite Material
Mech.
Strain
Magneti-
zation
Polarization
0-3 Type
2-2 Type
1-3 Type
0 for particle
1 for fiber
2 for layer
3 for matrix
H
magnetic mechanicalME effect
mechanical electric
E
electric mechanicalME effect
mechanical magnetic
Product Property:
▪ Magnetostrictive effect is a property of
ferromagnetic materials that causes them
to change their shape or dimensions during
the process of magnetization.
▪ Piezoelectric effect is the ability of certain
materials to generate an electric charge in
response to applied mechanical stress.
H
l
zΔ z
Magnetostrictive
layer
Piezoelectric
layer
Magnetostrictive
rod
Piezoelectric
plate
Δ z Fixed boundary with
rigid frame
M
M
P
M P
0
l 1 l 2
r
▪ Magnetostrictive nonlinear constitutive equation
Modelling
2m3 1(( ) )
2 3
ii s
iM
2 2( ) , ( )2
ss
s s
M M
M M
eH H M H
( ,H)E
0 0 ( ,H)B H M
2 2 2( ) , ( ) , ( )2 2
ys x s zx y z s
s s s
MM M
M M M
▪ Piezoelectric linear constitutive equation
Modelling
e e ec eE
T
eD e E
Implementation with COMSOL
Implementation with COMSOL
▪ Geometry
Implementation with COMSOL
Air block
NdFeB magnet
Magnetic pole
pieces
MS rod
PMN-PT plate
▪ Realization of PZT material model
▪ The linear constitutive equations for piezoelectric material
▪ For solid mechanics, the elastic relations
▪ For electrostatics, the electrical relations:
Implementation with COMSOL
0 0( ) eT
Es S c E
0( )rD D e E
1[( u) u]
2
T
s
VF
VD
E V
▪ Realization of magnetostrictive material model
▪ The elastic relations
Implementation with COMSOL
0( )Ec
0 ( , , )2 2 2
diag
Properties PMN–28PT
ρ, kg m-3 8060𝒄𝟏𝟏𝑬 ,GPa 115.4𝒄𝟏𝟐𝑬 ,GPa 103.4𝒄𝟏𝟑𝑬 ,GPa 102.6𝒄𝟑𝟑𝑬 ,GPa 114.1𝒄𝟒𝟒𝑬 ,GPa 68.9𝒄𝟔𝟔𝑬 ,GPa 65.8𝜺𝟏𝟏𝑺 /𝜺𝟎 925𝜺𝟑𝟑𝑺 /𝜺𝟎 813
𝒆𝟏𝟑,C m-2 -3.4𝒆𝟏𝟓,C m-2 10.1𝒆𝟑𝟑,C m-2 20.5
▪ Boundary conditions & Mesh
Implementation with COMSOL
Results
Thanks.