<HYPERELASTICITY> fung#

Description#

This model implements a Fung-type anisotropic hyperelastic behavior [M17] 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:

W(I3) = c2(expQ1)+K02[(I321)/2logI3]

where

Q=a~4×FbTFbI2Fb=FJ1/3

with I3=J2 the third invariant of the Green-Lagrange strain tensor and I the unity tensor. c, a~4 and K0 are the three material coefficients. K0 represents the Bulk modulus, while c is a material constant. a~4 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 [M18]:

***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