I am working to develop a model to represent the nanoindentation behavior of a viscoelastic material. I am able to get simulated load-displacement plot for random values of the model parameters. A suitable optimization algorithm is needed so that I can optimize the model parameters to give me minimum possible error between simulated and experimental P-h plots. If anyone can show me the ropes, I would greatly appreciate it.
There are many standard ways to do this - the term to search for is "inverse parameter identification"
You might also be interested in my recent publication
https://www.researchgate.net/publication/255723869_Inverse_parameter_identification_with_finite_element_simulations_using_knowledge-based_descriptors?ev=prf_pub
where I dealt with a similar problem (although it is a macroscopic indenter).
Article Inverse parameter identification with finite element simulat...
I don't think you can do this inverse analysis identification without using another software. In fact Abaqus will only simulate the indentation test with a given set of parameters, you should use an inverse analysis software that can will change the set of parameters in abaqus at each iteration. I know that ModeFrontier can do it but I don't know if you have a license. If you have the time you can program one using Python (free). Concerning the minimization algorithm you can use gradient methods (Newton-Raphson, Levenberg Marquardt, BFGS...) if you don't problem of unicity of solution (local and global minima) otherwise you can use alghorithme like simplex which may take a bit more iterations, combinig both will be ideal. Some o those method exists already in librarys of Python. I should mention that programming your own inverse analysis code may take a few weeks
There are many canned routines (for example the gnu scientific library) that can be used to do the actual optimisation - for moderately difficult problems, standard things like numerical recipes can be used. Of course you have to program the interface to abaqus.
For inverse analysis please try to use hyperstudy package where you can calibrate your material models of any fem package. There is a tutorial on material modelcalibration on you tube please check it out. Alternatively you could also try m-calibration , where you can calibrate any constitutive model as per fem software.
Have you considered a non-determinstic approach - e.g. use of Bayesian Inference for parameter estimation, or indeed model selection? There are a number of papers on the topic, an example from Mares, Dratz, Mottershead and Friswell can be found at:
https://pdfs.semanticscholar.org/336b/f84ee220b3c0e1c4a461580e32e2801701e6.pdf
Abaqus has built in features to calibrate your material and to fit coefficients on your material test data. It definitely works with the hyperelastic behaviour, which is a good start.
Look around here, this is the best site I've found so far in the topic of hyper/viscoelastics and simulation data:
https://polymerfem.com/forum/polymerfem-downloads/viscoelasticity
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