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 Subsubsection 4.2.1.4: Fiber with Toe-Linear Response Up Subsection 4.2.1: Unconstrained Fiber Models Subsection 4.2.2: Uncoupled Fiber Models 

4.2.1.5 Fiber Exp-Linear

This constitutive fiber model has an initial exponential rise and then grows linearly after a user-specified stretch transition point. This fiber material is based on the trans-iso Mooney-Rivlin model introduced in [73]. This material by itself is not stable, so it is recommend to use it as part of a solid mixture.
The strain energy is as follows: where is the exponential integral function. The resulting fiber stress is evaluated from Here, is the stretch at which the fibers are straightened, scales the exponential stresses, is the rate of uncrimping of the fibers, and is the modulus of the straightened fibers. is determined from the requirement that the stress is continuous at .
<c3> Exponential stress coefficient [P]
<c4> Fiber uncrimping coefficient [ ]
<c5> Modulus of straightened fibers [P]
<lambda> Fiber stretch for straightened fibers [ ]
<fiber> Fiber distribution option
Example:
<material id="1" name="Material" type="solid mixture">
  <solid type="neo-Hookean">
    <E>1e6</E>
    <v>0.32</v>
  </solid>
  <solid type="fiber-exp-linear">
    <c3>1</c3>
    <c4>1</c4>
    <c5>1</c5>
    <lambda>1.05</lambda>
    <fiber type="const">1,0,0</fiber>
  </solid>
</material>


 Subsubsection 4.2.1.4: Fiber with Toe-Linear Response Up Subsection 4.2.1: Unconstrained Fiber Models Subsection 4.2.2: Uncoupled Fiber Models