Mechanical Material Curve Fitting

The material curve fitting calculates coefficients of material models that approximate the following experimental data. You can enter the data or copy and paste data from a spreadsheet into the Table pane. See the Curve Fitting section for additional specification information.

Hyperelastic Test Data

  • Uniaxial Test f(T) (Engineering Strain vs. Engineering Stress)

  • Biaxial Test f(T) (Engineering Strain vs. Engineering Stress)

  • Shear Test f(T) (Engineering Strain vs. Engineering Stress)

  • Volumetric Test f(T)

The following hyperelastic material models support curve fitting of the experimental data. For additional information, see the Material Curve-Fitting chapter in the Mechanical APDL Material Reference.

  • Mooney-Rivlin

  • Ogden

  • Neo-Hookean

  • Polynomial

  • Yeoh

  • Arruda-Boyce

  • Gent

  • Blatz-Ko

Note:  The Volume Ratio equals the ratio of the current volume to that of the original volume and all solution data displayed for postprocessing are true stresses and logarithmic strains.

The experimental data defined for all temperatures is used for curve fitting. Ensure that temperatures are defined consistently for different experimental data. If the experimental data contains temperature mismatch, then the warning message is displayed in the Messages pane during Solve Curve Fit.

When volumetric data is supplied, a compressible or nearly incompressible model is implied. When no volumetric data is supplied, the model is understood to be incompressible. Supplying zero as a coefficient for the volumetric data also denotes an incompressible model. The curve fitting will calculate the parameters based on an incompressible model when volumetric data is supplied and also when calculating the Stress-Strain points for charting.

Perform curve fitting for the various hyperelastic models to choose the one, based on the range of strain you are interested in, that best matches the experimental data provided.

Chaboche Test Data

Uniaxial Plastic Strain Test Data f(T) (Plastic Strain vs. True Stress)

Note:  To use curve fitting with plasticity, the only experimental data supported is Uniaxial Plastic Strain Test Data. Experimental data for plasticity is path dependent. Multiple Uniaxial Plastic strain test data can be added from Uniaxial Plastic Strain –Additional Test Data group which is accessible in the Toolbox, when Uniaxial Plastic Strain Test Data is selected.

Chaboche Kinematic Hardening plasticity model supports curve fitting of the Uniaxial Plastic strain test data. For additional information, see the Material Curve-Fitting chapter in the Mechanical APDL Material Reference.

Viscoelastic Test Data

  • Shear Data- Viscoelastic f(T) (Time vs. Shear Modulus)

  • Bulk Data - Viscoelastic f(T) (Time vs. Bulk Modulus)

Note:  Both the above test data are path dependent. Multiple test data can be added from Viscoelastic - Additional Test Data group which is accessible in the Toolbox, when test data is selected.

Viscoelastic models with curve fitting support:

  • Prony Shear Relaxation, f(T)

  • Prony Volumetric Relaxation, f(T)

For additional information, see the Material Curve-Fitting chapter in the Mechanical APDL Material Reference.

Note:  A change in the Number of Terms on the Prony models updates the curve fitting coefficients to allow fitting for the desired number of terms. The calculated values in the curve fitting are normalized, when Copy Calculated Values to Property is selected. The normalization uses the following equations, which describe the relationship between the Prony Coefficient () and the corresponding coefficient generated in curve fitting (). is the number of terms computed. is the square root of and is the square root of . and are the shear modulus and bulk modulus at . This is done to keep all and values used in the property table positive.

(1)

(2)

(3)

(4)

Error Norm for Fit

The error norm can be set to use normalized or absolute error. Normalized error norm considers each experimental datum equally in computing the curve fit. It generally provides better results than the absolute error norm, but in some cases the absolute error norm is a better choice.

Nonlinear Fitting (Ogden, Gent and Chaboche Kinematic Hardening)

For nonlinear curve fitting you can provide seed values for the coefficients or you can fix these seed values. The seed values can be provided for each temperature data. If you do not provide seed values internal defaults is used. It is suggested that you attempt to use seed values based on experience if possible. The nonlinear curve fit most often converges to a local error norm minimum. It may take several attempts (trial seed values) to achieve the desired fit, or copying and pasting the last solution as seed values and solving again.

Curve fitting for viscoelastic models Prony Shear Relaxation and Prony Volumetric Relaxation is nonlinear.