hyper_elastic_mooney#
Description#
This model 1this behavior is Z-set specific, and therefore does not apply for
Z-mat for other codes implements a two coefficient Mooney-Rivlin hyperelastic
behavior including an additional coefficient for compressibility
treatment. The coefficients for the hyperelastic law are declared under
**mooney
.
Hyperelastic behavior here defines the strain energy density with the following form:
with \(I_1\), \(I_2\), and, \(I_3\) the first, second, and
third invariants of the Green-Lagrange strain tensor. moon1
,
moon2
and moon3
are the three material coefficients.
moon3
represents a dimensionless compressibility coefficient,
while moon1
and moon2
have the dimension of a stress.
The Piola-Kirchhoff stress tensor is written:
Thermal deformations may also be accounted for with the addition of a
**thermal_strain
option within the behavior definition to declare
thermal strain coefficients.
Syntax#
***behavior hyper_elastic_mooney
[ **thermal_strain <THERMAL_STRAIN> ]
**mooney
moon1
COEFFICIENT
moon2
COEFFICIENT
moon3
COEFFICIENT
[ **save_principle_strain ]
If the option **save_principle_strain
is given, the principle values
of the Green strain tensor will be stored in addition to the standard
variables. These are in order from the greatest (most positive) to the
smallest (biggest negative or smallest positive) in the variables
e1
, e2
, and e3
.
Compatible elements#
This material model is programmed to be used with all versions of the
total Lagrangian elements (element types starting with
total_lagrangian
). The behavior must therefore be used in
conjunction with a declaration of these elements in the .inp
file
(see ***mesh
under ****calcul
).
The stored variables for this model include the Green-Lagrange total strain tensor, the Cauchy stress tensor, and the strain energy density \(W\). As an auxiliary output variable, the Piola-Kirchhoff stress tensor is stored but not saved during the calculation (may be requested as output). The post-processor prefixes used for these variables are the following:
Example#
The following is a simple example of the hyperelastic Mooney model:
***behavior hyper_elastic_mooney
**mooney
moon1 0.34
moon2 0.0
moon3 500.
**save_principle_strain
***coefficient
masvol 0.95e-9
***return