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 Subsubsection 4.13.1.1: Uncoupled Prescribed Uniaxial Active Contraction Up Subsection 4.13.1: Contraction in Mixtures of Uncoupled Materials Subsubsection 4.13.1.3: Uncoupled Prescribed Isotropic Active Contraction 

4.13.1.2 Uncoupled Prescribed Transversely Isotropic Active Contraction

The material type for prescribed isotropic active contraction in a plane transverse to a given direction (or fiber), in an uncoupled solid mixture, is “prescribed trans iso active contraction uncoupled”. This material must be combined with a stable uncoupled material that acts as a passive matrix, using a “uncoupled solid mixture” container as described in Section 4.1.2.14↑. The following material parameters need to be defined:
<T0> representing the prescribed stress [P]
In the reference configuration, the fiber is oriented along the unit vector , where are orthonormal basis vectors representing the local element coordinate system when specified (Section 4.1.1↑), or else the global Cartesian coordinate system. The active stress for this material is given by where is the stretched fiber orientation in the current (deformed) configuration and is the left Cauchy-Green tensor.
Example:
Isotropic contraction in plane transverse to , in a mixture containing a Mooney-Rivlin solid.
<material id="1" type="uncoupled solid mixture">
  <mat_axis type="local">0,0,0</mat_axis>
  <solid type="Mooney-Rivlin">
    <c1>1.0</c1>
    <c2>0</c2>
    <k>1000</k>
  </solid>
  <solid type="prescribed trans iso active contraction uncoupled">
    <T0 lc="2">1</T0>
    <mat_axis type="angles">
      <theta>0</theta>
      <phi>90</phi>
    </mat_axis>
  </solid>
</material>
 Subsubsection 4.13.1.1: Uncoupled Prescribed Uniaxial Active Contraction Up Subsection 4.13.1: Contraction in Mixtures of Uncoupled Materials Subsubsection 4.13.1.3: Uncoupled Prescribed Isotropic Active Contraction