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Subsection 4.1.2: Uncoupled Materials Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.2: Ellipsoidal Fiber Distribution Uncoupled

#### 4.1.2.1 Arruda-Boyce

This material describes an incompressible Arruda-Boyce model [2]. The following material parameters are required:
 initial modulus [P] number of links in chain [ ] Bulk modulus [P]
The uncoupled strain energy function for the Arruda-Boyce material is given by: where, and the first invariant of the right Cauchy-Green tensor. The volumetric strain function is defined as follows, This material model was proposed by Arruda and Boyce [2] and is based on an eight-chain representation of the macromolecular network structure of polymer chains. The strain energy form represents a truncated Taylor series of the inverse Langevin function, which arises in the statistical treatment of non-Gaussian chains. The parameter is related to the locking stretch , the stretch at which the chains reach their full extended state, by .
Example:
<material id="1" type="Arruda-Boyce">
<mu>0.09</mu>
<N>26.5</N>
<k>100</k>
</material>


Subsection 4.1.2: Uncoupled Materials Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.2: Ellipsoidal Fiber Distribution Uncoupled