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18.104.22.168 Holzapfel-Gasser-Ogden Unconstrained
The material type for the unconstrained Holzapfel-Gasser-Ogden material  is HGO unconstrained. The following material parameters must be defined:
|<c>||Shear modulus of ground matrix||[P]|
|<k2>||Fiber exponential coefficient||[P]|
|<gamma>||Fiber mean orientation angle||[deg]|
The strain-energy function is given by: The fiber strain is where and . The Macaulay brackets around indicate that this term is zero when and equal to when this strain is positive.
There are two fiber families along the vectors ( ), lying in the plane of the local material axes , making an angle with respect to . Each fiber family has a dispersion , where . When there is no fiber dispersion, implying that all the fibers in that family act along the angle ; the value represents an isotropic fiber dispersion. All other intermediate values of produce a periodic von Mises fiber distribution, as described in . is the shear modulus of the ground matrix; is the fiber modulus and is the exponential coefficient.
Unlike the uncoupled Holzapfel-Gasser-Ogden material presented in Section 22.214.171.124↑, this unconstrained version does not enforce isochoric deformation. This unconstrained model may be used to describe the porous solid matrix of a biphasic or multiphasic tissue model, where pore volume may change in response to influx or efflux of interstitial fluid.
<material id="2" type="HGO unconstrained"> <c>7.64</c> <k1>996.6</k1> <k2>524.6</k2> <gamma>49.98</gamma> <kappa>0.226</kappa> <k>7.64e3</k> </material>