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Subsection 4.13.1: Contraction in Mixtures of Uncoupled Materials Up Subsection 4.13.1: Contraction in Mixtures of Uncoupled Materials Subsubsection 4.13.1.2: Uncoupled Prescribed Transversely Isotropic Active Contraction

#### 4.13.1.1 Uncoupled Prescribed Uniaxial Active Contraction

The material type for prescribed active contraction along a single direction (or fiber) in an uncoupled solid mixture is “uncoupled prescribed uniaxial active contraction”. 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:
 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.
Example:
Uniaxial contraction along , in a mixture containing a Mooney-Rivlin solid.
<material id="1" type="uncoupled solid mixture">
<mat_axis type="local">0,0,0</mat_axis>
<k>1000</k>
<solid type="Mooney-Rivlin">
<c1>1.0</c1>
<c2>0</c2>
</solid>
<solid type="prescribed uniaxial active contraction uncoupled">
<T0 lc="2">1</T0>
<mat_axis type="angles">
<theta>0</theta>
<phi>90</phi>
</mat_axis>
</solid>
</material>

Subsection 4.13.1: Contraction in Mixtures of Uncoupled Materials Up Subsection 4.13.1: Contraction in Mixtures of Uncoupled Materials Subsubsection 4.13.1.2: Uncoupled Prescribed Transversely Isotropic Active Contraction