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Piezoresistive effect and change in r...

# Piezoresistive effect and change in resistance due to geometrical change

Posted in the ANSYS Forum

cdev

Écury-sur-coole, France

#1 Sep 10, 2012
Dear all,

For a small project I am trying to simulate the change of resistance due to loading of a material. However, I am facing some issues. Following different test cases from the ANSYS help, I successfully obtained the change of resistance due to the piezoresistive effect. When I try to isolate (comment out the piezoresistive properties) the change of resistance due to the simple change of geometry caused by loading, I do not see any differences in resistance.

I think that the problem is coming from the fact that a first analysis should be performed to obtain the strain/stresses and a second to identify the electrical resistance.

dR/R = epsilon*[1+2*nu]+ droh/roh
where epsilon is the strain, nu is Poisson's ratio, droh/roh the piezo resistive effect.

Cédric

*****ANSYS CODE*****
FINISH
/CLEAR
/FILNAME,resistance,1
/RGB,INDEX,100,100,100,0
/RGB,INDEX,80,80,80,13
/RGB,INDEX,60,60,60,14
/RGB,INDEX,0,0,0,15

/PREP7

A=0.5
L=100
W=10
elsize=5
P=1000
E=165e3
nu=0.25
!Resistivity (p-type Si), Ohm*mm
rho=78
!Piezoresistive coefficients (p-type Si),(MPa)^1
p11=6.5e-5
p12=-1.1e-5
p44=138.1e-5

ET,1,PLANE223,101 ! piezoresistive element type

MAT,1
MP,EX,1,%E%
MP,PRXY,1,%nu%
MP,RSVX,1,%rho%

! piezoresistive stress matrix
!TB,PZRS,1
!TBDATA,1,p11,p12,p12
!TBDATA,7,p12,p11,p12
!TBDATA,13,p12,p12,p11
!TBDATA,22,p44

RECTNG,0,%L%,0,%W%

TYPE,1
ESIZE,%elsize%
MSHAPE,1,2-D
AMESH,1

! Left voltage
NSEL,S,LOC,X,0
CP,1,VOLT,all
F,ALL,AMPS,%A%
SF,ALL,PRES,%P%
*get,nl,node,0,num,min ! get master node
*get,nb,node,0,COUNT ! get node count

! Right voltage
NSEL,S,LOC,X,%L%
CP,2,VOLT,all
D,ALL,UX,0,,,,UY
D,ALL,VOLT,0 ! ground right electrode
*get,nr,node,0,num,min ! get master node

ALLSEL,ALL

/PBC,u,,1
/PBC,volt,,1
/PBC,cp,,1
/PNUM,TYPE,1
/NUMBER,1
EPLOT
FINI

/SOLU ! Solution
antype,static
cnvtol,amps,1,1.e-3 ! Optional to prevent a warning message
solve
fini

/POST1
/com,
/com, Results:
/com, Res =%abs(volt(nl)-volt(nr))/(A*nb )% Ohm
/com, ResOri =%rho*L/W% Ohm
/com, ResDif =%rho*L/W-abs(volt(nl)-volt(nr ))/(A*nb)% Ohm
fini

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