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What are the methods for assessing accuracy of FEM models?

That is, to guide the development of a FEM model, and finally for assessing its reliability, what kinds of practices are used?

Sometimes it might be impossible to compare a model to a real-world scenario, because such scenario may not exist.

What does one do in such situation?

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  • $\begingroup$ You need to be more specific and citing example(s) for your claim "Sometimes it might be impossible to compare a model to a real-world scenario, because such scenario may not exist." $\endgroup$
    – r13
    Jun 14, 2022 at 11:15
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    $\begingroup$ If you don’t have a real-world scenario then compare to a theoretical one. $\endgroup$
    – Solar Mike
    Jun 14, 2022 at 11:16
  • $\begingroup$ @r13 Ehh, isn't this quite evident that one might try modelling scenarios that one hasn't observed or cannot observe, but one speculates about their possibility. I.e. one models for the unseen risks (an earthquake, for example, or a misuse of equipment). $\endgroup$
    – mavavilj
    Jun 14, 2022 at 11:17
  • $\begingroup$ @SolarMike Then what's "accuracy" in that context? $\endgroup$
    – mavavilj
    Jun 14, 2022 at 11:19
  • $\begingroup$ As a practical example, consider if one wished to design a USB stick and a USB port that are very durable. Then how is one going to model all the possible types of forces that are applied to them? Still, USB equipment does break, so have they been tested enough? $\endgroup$
    – mavavilj
    Jun 14, 2022 at 11:20

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Usually the best way would be to start with a simple problem which has a solution --analytically or experimentally-- and validate the FEM results against the analytical solution or the experimental data.

Then move on to something more complex, and usually experimental validation is required.

Most FEM software have simple benchmark cases that if you go through the documentation you can find.

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  • $\begingroup$ "Most FEM software"? For example what software? $\endgroup$
    – mavavilj
    Jun 15, 2022 at 8:07
  • $\begingroup$ e.g. abaqus/simulia or ansys $\endgroup$
    – NMech ♦
    Jun 15, 2022 at 10:46
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You are conflating two different things:

  1. Proof that your mathematical model is an accurate enough description of physical reality
  2. Proof that your numerical model is an accurate enough description of the mathematical model

For the first, you run physical validation experiments (using a design of experiments to cover a large enough range of possibilities) and compare the collected data with numerical simulation results. These numerical simulations can be as complex as needed and may include physics + chemistry.

For the second, you find analytical solutions or numerical solutions that are of high degree of accuracy and compare your numerical results. Ideally, your numerical method must be an accurate representation of the mathematical model and that is what most commercial codes do to get certified (for nuclear plant design, for example).

Whether the mathematical model is good enough is a different ball game and is typically determined via both new theory and experiment developments.

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