How can I know my simulation is quasi-static or not?

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As a rule of thumb, a simulation is static or quasi-static if the excitation frequency is less than 1/10 of the lowest natural frequency of the structure. This is mentioned in Abaqus Documentation:

It is usually desirable to increase the loading time to 10 times the period of the lowest mode to be certain that the solution is truly quasi-static.

In a static or quasi-static analysis, the lowest mode of the structure usually dominates the response. Therefore, knowing the frequency and, correspondingly, the period of the lowest mode, you can estimate the time required to obtain the proper static response. The natural frequencies can be calculated easily using the eigen frequency extraction procedure in Abaqus/Standard (Frequency analysis).

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