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Electrical Conductivity as a function of Electric Field

Posted Sep 20, 2012, 10:52 a.m. EDT Version 5.1 3 Replies

John Schmidt
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Following some technical literature on the topic of a conductivity of a material (specifically a polymer) that is based on electric field, I wish to model this in COMSOL. In case you are curious, the paper I am referring to is: "Effect of Insulation Properties on the Field Grading of Solid Dielectric DC Cable" by Boggs, et al (IEEE Transactions on Power Delivery, Vol 16, No 4, Oct 2001). I am referring to equation 1, 5,6. Basically, conductivity is based on electric field and temperature. For my model, I would like to keep the temperature constant right now. I would like to, however, make electrical conductivity anisotropic and as a function as electric field (in the X-direction and Y-direction). This "seems" easy to do, and I have already made a quick model showing this (which I have attached as well). The conductivities are defined in the Global Definitions -> Variables 1a. When I try to solve, I get an error: "Undefined value found.
- Detail: Undefined value found in the equation residual vector.
.There are 1217 degrees of freedom giving NaN/Inf in the vector for the variable mod1.V"

This error is from the fact that I have conductivity as an electric field. If I change the conductivity to being a constant, there is no problem.


Thank you in advance for any help you can give me.
John
3 Replies Last Post Sep 22, 2016, 8:00 p.m. EDT
Nils Malm COMSOL Employee

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Posted: 1 decade ago Sep 25, 2012, 4:26 a.m. EDT
Hello John,
The error message you have encountered is usually caused by a division by zero somewhere in your expressions. In particular, if your conductivity expressions cannot be evaluated when the potential is constant (electric field is zero) you will encounter this problem already in the first solver iteration if your initial condition for the potential is constant.

If you expect the electric field to be nonzero everywhere, you can try to use some approximation of the expected field as initial condition (e.g., use a solution obtained with fixed conductivity). You may also want to try modifying expressions, e.g., by adding small offsets in denominators.

best regards
Nils Malm
COMSOL AB
Hello John, The error message you have encountered is usually caused by a division by zero somewhere in your expressions. In particular, if your conductivity expressions cannot be evaluated when the potential is constant (electric field is zero) you will encounter this problem already in the first solver iteration if your initial condition for the potential is constant. If you expect the electric field to be nonzero everywhere, you can try to use some approximation of the expected field as initial condition (e.g., use a solution obtained with fixed conductivity). You may also want to try modifying expressions, e.g., by adding small offsets in denominators. best regards Nils Malm COMSOL AB
John Schmidt
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Posted: 1 decade ago Sep 25, 2012, 6:07 p.m. EDT
Thank you Nils, that seems to solve my problem!! I simply made an initial condition for potential that was non-zero and then added a very small offset in the denominator.

Regards,
John


Hello John,
The error message you have encountered is usually caused by a division by zero somewhere in your expressions. In particular, if your conductivity expressions cannot be evaluated when the potential is constant (electric field is zero) you will encounter this problem already in the first solver iteration if your initial condition for the potential is constant.

If you expect the electric field to be nonzero everywhere, you can try to use some approximation of the expected field as initial condition (e.g., use a solution obtained with fixed conductivity). You may also want to try modifying expressions, e.g., by adding small offsets in denominators.

best regards
Nils Malm
COMSOL AB


Thank you Nils, that seems to solve my problem!! I simply made an initial condition for potential that was non-zero and then added a very small offset in the denominator. Regards, John [QUOTE] Hello John, The error message you have encountered is usually caused by a division by zero somewhere in your expressions. In particular, if your conductivity expressions cannot be evaluated when the potential is constant (electric field is zero) you will encounter this problem already in the first solver iteration if your initial condition for the potential is constant. If you expect the electric field to be nonzero everywhere, you can try to use some approximation of the expected field as initial condition (e.g., use a solution obtained with fixed conductivity). You may also want to try modifying expressions, e.g., by adding small offsets in denominators. best regards Nils Malm COMSOL AB [/QUOTE]
Rishad Arfin
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Posted: 8 years ago Sep 22, 2016, 8:00 p.m. EDT
Hey John and Nils,

I would like to design a material just like you did long ago. I am doing simulation in time domain, where the material anisotropic conductivity depends on the electric field. Would you please suggest me how to define the anisotropic conductivity matrix in the material section ?

Moreover, my sigma depends on Ey and Ex, how can I define the dependency in time domain ? Please kindly let me know.

Thanks,
Rishad
Hey John and Nils, I would like to design a material just like you did long ago. I am doing simulation in time domain, where the material anisotropic conductivity depends on the electric field. Would you please suggest me how to define the anisotropic conductivity matrix in the material section ? Moreover, my sigma depends on Ey and Ex, how can I define the dependency in time domain ? Please kindly let me know. Thanks, Rishad

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