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Subsection 4.13.2: Contraction in Mixtures of Unconstrained Materials Up Subsection 4.13.2: Contraction in Mixtures of Unconstrained Materials Subsubsection 4.13.2.2: Prescribed Transversely Isotropic Active Contraction

#### 4.13.2.1 Prescribed Uniaxial Active Contraction

The material type for prescribed active contraction along a single direction (or fiber) in a solid mixture of unconstrained materials is “prescribed uniaxial active contraction”. This material must be combined with a stable compressible material that acts as a passive matrix, using a “solid mixture” container as described in Section 4.1.3.22↑. 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 neo-Hookean solid.
<material id="1" type="solid mixture">
<mat_axis type="local">0,0,0</mat_axis>
<solid type="neo-Hookean">
<E>1.0</E>
<v>0.3</v>
</solid>
<solid type="prescribed uniaxial active contraction">
<T0 lc="2">1</T0>
<mat_axis type="angles">
<theta>0</theta>
<phi>90</phi>
</mat_axis>
</solid>
</material>

Subsection 4.13.2: Contraction in Mixtures of Unconstrained Materials Up Subsection 4.13.2: Contraction in Mixtures of Unconstrained Materials Subsubsection 4.13.2.2: Prescribed Transversely Isotropic Active Contraction