Analysis and solution-control information for calibration and validation follow:
Material parameter calibration occurs using the curve-fitting tool.
Example 15.1: Fitting a Hyperelastic Constitutive Model to a Set of Uniaxial Stress-Strain Data
The command input shown here is for illustration only. While curve-fitting is possible via command input, Ansys, Inc. recommends using the graphical user interface (GUI) to perform the curve-fitting, or at least visually validating the results using the GUI to ensure a sound fit.
/PREP7 TBFT,FADD,1,HYPER,MOONEY,3 TBFT,EADD,1,UNIA,UNIAX.LOG TBFT,SOLVE,1,HYPER,MOONEY,3 TBFT,FSET,1,HYPER,MOONEY,3
The TBFT,FADD command initializes the curve-fitting procedure for a hyperelastic, three-parameter, Mooney-Rivlin model assigned to material identification number 1.
TBFT,EADD reads the uniaxial experimental data in the uniax.log file as the fitting data for material number 1. The experimental data in the file is a set of engineering-strain vs. engineering-stress input:
0.819139E-01 0.82788577E+00 0.166709E+00 0.15437247E+01 0.253960E+00 0.21686152E+01 0.343267E+00 0.27201819E+01 0.434257E+00 0.32129833E+01 0.526586E+00 0.36589498E+01 0.619941E+00 0.40677999E+01 0.714042E+00 0.44474142E+01 0.808640E+00 0.48041608E+01 0.903519E+00 0.51431720E+01 0.998495E+00 0.54685772E+01 0.109341E+01 0.57836943E+01
TBFT,SOLVE determines the three constitutive parameters for the Mooney-Rivlin model, minimizing the difference between the model and the experimental data.
TBFT,FSET assigns the fitted constitutive parameters to material number 1.
For this problem, the fitted parameters for the three-parameter Mooney-Rivlin model are:
C10 =
1.338856 |
C01 = 5.236214 x
10-1 |
C11 = - 1.648364 x
10-2 |
Following is a mesh developed to simulate the torsion experiment to validate the fitted constitutive model parameters obtained in Calibrating Parameters:
The mesh consists of 1,332 SOLID186 elements using the default formulation (a mixed-displacement pressure formulation with reduced integration).
The attachment of the test specimen to the test apparatus is simulated by boundary conditions applied to the specimen in the region of the clamps, as described here:
The back-left clamp region is fully restrained.
The back-right clamp region is attached to a rigid-contact surface and fixed in place.
The front-left clamp region is attached to a rigid-contact surface and displaced in the z direction to simulate a clamping displacement equal to 25 percent of the specimen thickness. The same is true for the front-right clamp region.
The stretching to 50 percent engineering strain is simulated by displacing the rigid-contact surfaces attached to the right clamp regions while holding left clamp regions fixed.
The torsion of the specimen is simulated by holding the left clamp region in place and twisting the keypoints attached to the right contact surfaces about the longitudinal axis.