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Theory Manual Version 3.6
 Subsection 5.3.5: Transversely Isotropic Hyperelastic Up Section 5.3: Nearly-Incompressible Materials Subsection 5.3.7: Fiber with Exponential Power Law Uncoupled 

5.3.6 Ellipsoidal Fiber Distribution

This constitutive model describes a material that is composed of an ellipsoidal continuous fiber distribution in an uncoupled formulation. The deviatoric part of the stress is given by [6, 9, 63], and the corresponding elasticity tensor is is the square of the fiber stretch , is the unit vector along the fiber direction (in the reference configuration), which in spherical angles is directed along , and is the unit step function that enforces the tension-only contribution. The fiber stress is determined from a fiber strain energy function in the usual manner: whereas the fiber elasticity tensor is where in this material The materials parameters and are determined from: Since fibers can only sustain tension, this material is not stable on its own. It must be combined with a material that acts as the ground matrix. The total stress is then given by the sum of the fiber stress and the ground matrix stress:
 Subsection 5.3.5: Transversely Isotropic Hyperelastic Up Section 5.3: Nearly-Incompressible Materials Subsection 5.3.7: Fiber with Exponential Power Law Uncoupled