Load curves for non-linear studies

Hi,

I'm studying a difficult non-linear problem where I need a very smooth load/unload curve (displacement vs time).

There are several instabilities in the solution, therefore loading/unloading should occur very slow.

I tought about using a Gaussian function, it almost does the job, altough you need to adjust it in the beginning and at the end.

Do you have any suggestions of possible mathemathical functions that can be good for a slow loading/unloading ?

I'm attaching the Excel spreadsheet I've used to build a load/unload curve where total time is 2 seconds, loading starts at o sec and ends at 1 sec. Unloading is from 1 sec to 2 sec

SolidworksSimulation