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a unit syntax error while trying to define a parameter with fractional powers in the units

Posted 2025年2月4日 GMT+8 18:38Modeling Tools & DefinitionsVersion 5.51 Reply

Vishnu Abhinav
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I am using COMSOL 5.5. While trying to simulate a simple temperature dependent resistance simulation, I am facing an issue of fractional power of the unit in the parameter section. How to resolve this?

A = 1.08e31 [1/cm^3/K^(3/2)]

Please.

1 Reply Last Post 2025年2月4日 GMT+8 21:20
Henrik Sönnerlind COMSOL Employee

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Posted: 2 years ago 2025年2月4日 GMT+8 21:20

The best approach is to reformulate the problem, so that you use an auxiliary reference value.

Attached is a screenshot showing how this is handled for the built-in Norton creep law. Usually this law is written as

whereis the strain,is the stress, andnis a power that is usually not an integer. This causes the coefficientAto have awkward units. (There are other problems too, for example you must know the unit in which the stress is measured.)

In order to avoid non-integer powers of units, we introduce an arbitrary reference stress, so that the equation is transformed into

Then,Awill always have the unit 1/s. It will also not change its value if you change the unit system for the stress.

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Henrik Sönnerlind
COMSOL
The best approach is to reformulate the problem, so that you use an auxiliary reference value. Attached is a screenshot showing how this is handled for the built-in Norton creep law. Usually this law is written as \frac {d \varepsilon}{dt} = A \sigma^n where \varepsilon is the strain, \sigma is the stress, and *n* is a power that is usually not an integer. This causes the coefficient *A* to have awkward units. (There are other problems too, for example you must know the unit in which the stress is measured.) In order to avoid non-integer powers of units, we introduce an arbitrary reference stress, so that the equation is transformed into \frac {d \varepsilon}{dt} = A (\frac{\sigma}{\sigma_{ref}})^n Then, *A* will always have the unit 1/s. It will also not change its value if you change the unit system for the stress.

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