In early 2015, Li Zhang was working on a Fortran program to perform simultaneous and integrated Hyper+Prony calibration. But with that process, you could not see any stress-strain plots until the calibration was completely finished. To prototype a calibration process with good graphics capability, we re-cast the integrated equations into Excel. This Excel work was also done in early 2015, but only recently posted here.
In this post I have attached 2 Isight models. The first will focus on some "psuedo-data", for which we know the right answer. The second will focus on some real elastomer data, using a family of rate curves. These Isight models and the Excel file were created to prototype the approach to calibrating a Hyper+Prony model from a family of rate data, and generally, any arbitrarily varying time-strain history. Be careful with the Excel file, the many columns of equations can be easily broken.
Sometimes it is hard to share the Isight .zmf file because of the way it references other files. The default Isight behavior is to reference by absolute path name. Another option is to reference by relative path name, and another choice is build the auxiliary file (Excel in this case) directly into the .zmf file. I have used the 3rd option. This 3rd option means the .zmf file should be very easily usable by you. But if you change the Excel file, then you need to “reload” the Excel file into the .zmf file. These .zmf models were created using Isight version 5.9-2.
Psuedo-test Data
The "pseudo-test data" was generated by running a series of Abaqus unit-cube models with different types of loading. All the pseudo-test data was generated using the same Yeoh+Prony material model. This underlying Yeoh+Prony model was a reasonable elastomer material model generated from some test data taken during one of our elastomer classes at Axel Products. This material model is fully incompressible. There is a single zip file attached which contains all the files for this case.
This image is also included in the zip file (Excel_Prototype_Yeoh_Prony_5gs_Start.png). The pseudo-test data is shown in dots, and the math stress response is shown with lines. This image shows the starting guess for the Yeoh+Prony model.
There is an attached zip file named "Pseudo-test_Data.zip" that contains 3 .zmf Isight model files, the Excel file, and a few other images. The reason for 3 .zmf files is because we have run this case with the Hooke-Jeeves optimizer, but set the number of iterations to 1000, then 2000, then 3000. These 3 cases run in about 3 minutes, 5 minutes, and 8 minutes on my Win7 laptop. One of the images in the zip file shows the errors produced when the known answer is entered, see file named Yeoh_Prony_Prototype_Cal2_test-with-right-answer.png In all of these cases, we have designated the Yeoh parameters, C10, C20, C30 and the 5 Prony g terms as design variables. The Prony tau terms remain fixed.
Real Rubber Test Data
This real rubber test data is a family of 5 simple tension pull-tests at various rates. This type of test data is commonly collected by people interested in drop testing, or crash testing, or other types of impact events. One interesting observation of the test data is the clear separation of the various curves all the way down to small strains. This clear separation suggests to us that the time-dependence in the material can be represented well by linear viscoelasticity.
As for the pseudo-test data case, we embed in Excel the equations to predict the stress from an arbitrary time varying strain history. This was quite tedious and was done just to prototype this solution methodology. The attached zip contains a variety of Isight .zmf files, each one using a different optimizer. We have also used different runs to look at the outcome of using an NMAD error norm versus a SSE error norm. There is a summary of all of the optimizations performed in the worksheet labeled "Opt. History" in the Excel file named "Yeoh_Prony_Butyl_Cal_Finish.xlsx". We also note the run times of each optimizer.
Back to: Material Modeling and Calibration - An Overview and Curriculum
