<ISOTROPIC_HYPERELASTICITY> mooney

Description

This model implements a two coefficient Mooney-Rivlin hyperelastic behavior [M11] including an additional coefficient for compressibility treatment. The coefficients for the hyperelastic law are declared under **isotropic_hyperelasticity mooney.

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

(422)\[\begin{aligned} W(I_1,I_2,I_3)~=~&{\tt C10} (I_1 - 1) + {\tt C01}(I_2 - 1) + \dfrac{{\tt K0}}{2}[(I^2_3-1)/2-{\tt log}(I_3)] \end{aligned}\]

with \(I_1\), \(I_2\), and, \(I_3\) the first, second, and third invariants of the Green-Lagrange strain tensor. C10, C01 and K0 are the three material coefficients. K0 represents the Bulk modulus, while C10 and C01 have the dimension of stress.

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

Syntax

**isotropic_hyperelasticity mooney **model_coef \(~\,~\,\) C10 <COEFFICIENT> \(~\,~\,\) C01 <COEFFICIENT> \(~\,~\,\) K0 <COEFFICIENT>

Example

The following is a simple example of the hyperelastic Mooney model ^{1 1}The model parameters have been taken from [M12]:

***behavior hyper_elastic
 **isotropic_hyperelasticity mooney
 **model_coef
    C10            0.7
    C01            0.1
    K0          1000.
***return