Hyperelasticity:

• Figure, Interactive Fitting of Hyperelasticity (14kB)

Demonstrated is a subjective, interactive fitting exercise for hyperelasticity. Orthotropy is assumed for the exercise. Isotropy is realized by linking the six deviatoric strain energy functions located along the right edge (they then adjust in unison). The strain energy functions are manipulated with the mouse/cursor and the ten responses are continuously updated. When available, test data is shown with symbols on the corresponding response plot.

The manual/subjective fitting strategy addresses the following shortcomings of traditional least squares fitting:

• Limited or even no test data is required to achieve stable responses. Constant values of the strain energy functions set to shear and bulk moduli are analogous to generalized Hooke's law in the neighborhood of zero strain.
• High-order functions (up to three inflection points) are established which may be matched to high-order test data which is otherwise deficient in multi-axiality. Typically, high-order least squares fitting requires multi-axial test data to achieve stable fits.
• Stable, plausible, orthotropic functions may be generated with only limited test data, for example, uniaxial data in each of the three principal directions.