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Temperature-Dependent Thermal Expansion in the PolyUMod TNV

Introduction

I have written a number of article about the PolyUMod TNV model (Introduction, Temperature-Dependent Calibration), but I was recently asked to explain how to add temperature-dependent thermal expansion into the TNV, and this is a topic that I have not talked about. In this article I will show how to add temperature-dependent thermal expansion in the TNV model.

Initial Notes

  • All commercial FE solvers support temperature-dependent thermal expansion, but unfortunately the FE solver thermal expansion commands are not active when using a user-material model (like the PolyUMod library). This has always surprised me since it would be easy to enable that support in a FE solver.
  • If you are using Ansys Mechanical then I recommend that you calibrate a TNV model for each temperature of interest, and that you add constant thermal expansion for each temperature. Then provide the set of TNV model parameters for each temperature, and let ANSYS interpolate those parameters based on the actual temperature. This works great and is the easiest solution if you use Ansys. It is too bad that other FE solvers do not support this for user-material models.
  • For all other FE solvers I recommend that you use the PolyUMod Multi-Temperature Model.

PolyUMod Multi-Temperature Model

The PolyUMod Multi-Temperature model is a way to make any PolyUMod material model temperature-dependent. This model framework allows you to specify a set of material parameters for each temperature of interest, and then PolyUMod will interpolate between those sets based on the actual temperature.

To get temperature-dependent thermal expansion you simply need to specify a non-zero thermal expansion coefficient for each temperature. The PolyUMod Multi-Temperature model will then interpolate those values to get the desired response.

The video below shows how you can quickly set this up in MCalibration.

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