<ISOTROPIC_HYPERELASTICITY> neo_hookean#

Description#

This model implements the simplest physically based hyperelastic behavior [M14], the Neo-Hookean model, including an additional coefficient for compressibility treatment. The coefficients for the hyperelastic law are declared under **isotropic_hyperelasticity neo_hookean.

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

(424)#\[\begin{aligned} W(I_1,I_3)~=~&\frac{1}{2}{\tt nkT} (I_1 - 1) + \dfrac{{\tt K0}}{2}[(I^2_3-1)/2-\log{I_3}] \end{aligned}\]

with \(I_1\) and \(I_3\) the first and third invariants of the Green-Lagrange strain tensor. mu\(=\)nkT and K0 are the two material coefficients. K0 represents the Bulk modulus, while nkt is the material Shear modulus.

This model is in good agreement with tensile, simple shear and biaxial tests for deformation lower than 50%.

Syntax#

**isotropic_hyperelasticity neo_hookean **model_coef \(~\,~\,\) mu <COEFFICIENT> \(~\,~\,\) K0 <COEFFICIENT>

Example#

The following is a simple example of the hyperelastic Neo_hookean model 1The model parameters have been taken from [M14]:

***behavior hyper_elastic
 **isotropic_hyperelasticity neo_hookean
 **model_coef
    mu             0.4
    K0          1000.
***return