The strain-energy function for this constitutive model is defined by $$W=c_{1}\left(I_{1}-3\right)+c_{2}\left(I_{2}-3\right)-2\left(c_{1}+2c_{2}\right)\ln J+F\left(\lambda\right)+U\left(J\right)$$ The first three terms define the coupled Mooney-Rivlin matrix response. The third term is the fiber response which is a function of the fiber stretch $\lambda$ and is defined as in [58]. For $U$ , the following form is chosen in FEBio. $$U\left(J\right)=\frac{1}{2}k\left(\ln J\right)^{2}$$ where $J=\det\mathbf{F}$ is the Jacobian of the deformation.

Example:

<material id="1" type="coupled trans-iso Mooney-Rivlin">
  <c1>1</c1>
  <c2>0.1</c2>
  <c3>1</c3>
  <c4>1</c4>
  <c5>1.34</c5>
  <lam_max>1.3</lam_max>
  <k>100</k>
</material>