<HYPERELASTICITY> fung#

Description#

This model implements a Fung-type anisotropic hyperelastic behavior [M20] including an additional coefficient for compressibility treatment. The coefficients for the hyperelastic law are declared under **hyperelasticity fung.

Hyperelastic behavior here defines the strain energy density with the following form:

\[\begin{aligned} W(I_3)~=~&\frac{{\tt c}}{2} (\exp{Q} - 1) + \dfrac{{\tt K0}}{2}[(I^2_3-1)/2-\log{I_3}] \end{aligned}\]

where

\[\begin{split}\begin{aligned} Q&= \ten E_b :\tenf b: \ten E_b\\ \ten E_b &= \dfrac{1}{2}\left(\ten F^T_b\ten F_b - \ten I\right)\\ \ten F_b &= \frac{\ten F}{J^{1/3}} \end{aligned}\end{split}\]

with \(I_3 = J^2\) the third invariant of the Green-Lagrange strain tensor and \(I\) the unity tensor. The material coefficients are c, \(\tenf b\) and K0. K0 represents the Bulk modulus, while c is a material constant. \(\tenf b\) is the 4th order tensor of orientation.

This model of strain energy is classically used for very large strain biomechanics-related problems.

Syntax#

**hyperelasticity fung **model_coef \(~\,~\,\) c COEFFICIENT \(~\,~\,\) K0 COEFFICIENT \(~\,\) *b orthortropic \(~\,~\,\) y1111 COEFFICIENT \(~\,~\,\) y1122 COEFFICIENT \(~\,~\,\) y2222 COEFFICIENT \(~\,~\,\) y1133 COEFFICIENT \(~\,~\,\) y2233 COEFFICIENT \(~\,~\,\) y3333 COEFFICIENT \(~\,~\,\) y2323 COEFFICIENT \(~\,~\,\) y3131 COEFFICIENT \(~\,~\,\) y1212 COEFFICIENT

Example#

The following is a simple example of the hyperelastic Fung-type model 1The model parameters have been taken from [M21]:

***behavior hyper_elastic
 **hyperelasticity fung
 **model_coef
    c             26.95e-1
    K0          1000.
   *b orthotropic
   y1111           0.0089
   y1122           0.0193
   y2222           0.4180
   y1133           0.0295
   y2233           0.0749
   y3333           0.9925
   y2323           0.5
   y3131           0.5
   y1212           0.5
***return