Theory Manual Version 3.4
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Subsection 5.3.6: Ellipsoidal Fiber Distribution Up Section 5.3: Nearly-Incompressible Materials Subsection 5.3.8: Fung Orthotropic

### 5.3.7 Fiber with Exponential Power law

This material model describes a constitutive model for fibers, where a single fiber family follows an exponential power law strain energy function. The deviatoric part of the Cauchy stress is given by: and the corresponding spatial elasticity tensor is where is the square of the fiber stretch, is the fiber orientation in the reference configuration, and and is the unit step function that enforces the tension-only contribution. The fiber strain energy density is given by where , and .
Note: In the limit when , this expression produces a power law, Note: When , the fiber modulus is zero at the strain origin (. Therefore, use when a smooth transition in the stress is desired from compression to tension.
Subsection 5.3.6: Ellipsoidal Fiber Distribution Up Section 5.3: Nearly-Incompressible Materials Subsection 5.3.8: Fung Orthotropic