During working on soft tissue experiments, I need to try inverse finite element characterization and I need to check all disadvantages/limitations of this method.
It is alluring in it simplicity to believe that the more complex my model with the more possibilities to adjust, the better I shall catch the situation when using inverse methods.
The grim reality of any inverse method is that we are trying to solve a situation where you for a fact know that the answer is, say, 4 and all you have to figure out is - what was the question. This is a situation with an infinite numbers of solutions. You can pick any solution you like, for any reason you like, but - it will likely be wrong.
The better way is to use a forward approach where you search for a best fit using first principles, e.g. where you cut your samples into small test pieces and run these through whatever kinds of standard tests you are able to make to produce realistic engineering data.
Start with very simple tests and work from there to more complex test, e.g. start with weight, dimension change from static load, bounce a sample to find damping and so on. Do not settle for a single test, repeat them using different samples and sizes.
Your model becomes credible only when you can find engineering data for one situation and successfully use it to predict several other situations that largely differ in, say, load type, geometry etc.
I am not trying to sound pessimistic but my experience is that it is so easy to fool oneself.