<HYPERELASTICITY> ogden#
Description#
This model implements the Ogden’s phenomenological theory of elasticity
[M13] including an additional coefficient for
compressibility treatment. The strain energy density is written in terms
of generalized strain. The coefficients for the hyperelastic law are
declared under **hyperelasticity ogden
.
Hyperelastic behavior here defines the strain energy density with the following form:
where the material parameters \((\mu_n,\alpha_n)_{n=1,N}\) should fulfilled the following stability condition:
with \(\lambda_1\), \(\lambda_2\), and, \(\lambda_3\) the
three generalized stretches and \(I_3\) the third invariant of the
Green-Lagrange strain tensor. \(\mu_n\),
\(\alpha_n\) and K0
are the three material
coefficients. K0
represents the Bulk modulus, while
\(\mu_n\) and \(\alpha_n\) are
material constants.
This model is possibly the most extended model after Mooney-Rivlin model. Even if the determination of material parameters leads to some difficulties, this model is one of the most widely used for large strain problems.
Syntax#
**hyperelasticity ogden
**model_coef
\(~\,\) *term
\(~\,~\,\) mu
COEFFICIENT
\(~\,~\,\) alpha
COEFFICIENT
\(~\,~\,\) K0
COEFFICIENT
\(~\,\) *term
\(~\,~\,\) mu
COEFFICIENT
\(~\,~\,\) …
Example#
The following is a simple example of the hyperelastic Ogden model 1The model parameters have been taken from [M14]:
***behavior hyper_elastic
**hyperelasticity ogden
**model_coef
*term
mu 0.63
alpha 1.3
K0 10000.
*term
mu 1.2e-3
alpha 5.0
*term
mu -1.e-2
alpha -2.0
***return