<HYPERELASTICITY> ristinmaa

Description

This hyperelastic model is a modified St Venant-Kirchhoff model proposed by [], which is defined by a strain energy \(W\) as

(410)\[W(\ten E)=\dfrac{K}{2}(\log{J})^2+\mu~(\log \ten U)^{dev}:(\log \ten U)^{dev}\]

where the material parameters K and \(\mu\) correspond in the limit of small strains to the bulk and the shear modulus, respectively, \((\log U)^{dev}\) is the deviatoric part of the logarithm of the Hencky strain tensor \(U= C^{1/2}\) and \(J=det~F\). The second Piola-Kirchhoff stress tensor can be obtained as

(411)\[\ten S=\dfrac{dW}{d \ten E}=\lambda\log(J)C^{-1}+2\mu \log(\ten U)C^{-1}\]

where \(\ten C\) is the right Cauchy-Green deformation tensor.

Syntax

***behavior hyper_elastic \(~\,\) **hyperelasticity ristinmaa \(~\,~\,\) *elasticity \(~\,~\,~\,\) young <COEFFICIENT> \(~\,~\,~\,\) poisson <COEFFICIENT>

Example

The following is a simple example of Ristinmaa model. The user can supply either \((\lambda,\mu)\) or \((E,\nu)\).

***behavior hyper_elastic
 **hyperelasticity ristinmaa
  *elasticity
   mu           80000.
   lambda       121000.
***return