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The material type for the uncoupled Holzapfel-Gasser-Ogden material  is Holzapfel-Gasser-Ogden. 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]|
This material model uncouples deviatoric and volumetric behaviors. The deviatoric strain-energy function is given by: where and the default volumetric strain energy function is 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.
<material id="2" type="Holzapfel-Gasser-Ogden"> <c>7.64</c> <k1>996.6</k1> <k2>524.6</k2> <gamma>49.98</gamma> <kappa>0.226</kappa> <k>1e5</k> </material>