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

Posted Feb 4, 2025, 5:38 a.m. EST Modeling Tools & Definitions Version 5.5 1 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 Feb 4, 2025, 8:20 a.m. EST
Henrik Sönnerlind COMSOL Employee

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Posted: 6 months ago Feb 4, 2025, 8:20 a.m. EST

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

where is the strain, 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

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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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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