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Subsubsection 4.1.3.26: Coupled Transversely Isotropic Veronda-Westmann Up Subsection 4.1.3: Unconstrained Materials Section 4.2: Fibers

#### 4.1.3.27 Large Poisson's Ratio Ligament

This material describes a coupled, transversely isotropic material that will conform to a particular Poisson's ratio when stretched along the fiber direction [53]. The following material parameters must be defined:
 c1 Fiber coefficient c2 Fiber coefficient mu Matrix coefficient v0 Poisson's ratio parameter m Poisson's ratio parameter k Volumetric penalty coefficient
The strain energy function for this constitutive model is a three part expression: where: In the equations above, is the stretch ratio of the material along the fiber direction. The desired Poisson's ratio must first be selected based on available data for uniaxial tension along the fiber direction. The function with which to fit the Poisson's ratio data is: The volumetric penalty coefficient must be selected to be large enough to enforce the Poisson's function above. If this material is to be used in a biphasic representation, must be selected based on experimental stress-relaxation data, since has an effect on the biphasic behavior of the material. Once , , and are chosen, , and should be selected by fitting the stress-strain behavior of the material to experimental data. The Cauchy stress of the material is given by: where is the jacobian of the deformation gradient , is the left Cauchy-Green deformation tensor, is the identity tensor, is the fiber orientation vector in the deformed configuration.
Example:
<material id="1" name="Material1" type="PRLig">
<c1>90</c1>
<c2>160</c2>
<mu>0.025</mu>
<v0>5.85</v0>
<m>-100</m>
<k>1.55</k>
</material>


Subsubsection 4.1.3.26: Coupled Transversely Isotropic Veronda-Westmann Up Subsection 4.1.3: Unconstrained Materials Section 4.2: Fibers