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Subsubsection 4.13.2.1: Prescribed Uniaxial Active Contraction Up Subsection 4.13.2: Contraction in Mixtures of Unconstrained Materials Subsubsection 4.13.2.3: Prescribed Isotropic Active Contraction

4.13.2.2 Prescribed Transversely Isotropic Active Contraction

The material type for prescribed isotropic active contraction in a plane transverse to a given direction (or fiber), in a solid mixture of unconstrained materials, is “prescribed trans iso 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 and is the left Cauchy-Green tensor.
Example:
Isotropic contraction in plane transverse to , 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 trans iso active contraction">
<T0 lc="2">1</T0>
<mat_axis type="angles">
<theta>0</theta>
<phi>90</phi>
</mat_axis>
</solid>
</material>

Subsubsection 4.13.2.1: Prescribed Uniaxial Active Contraction Up Subsection 4.13.2: Contraction in Mixtures of Unconstrained Materials Subsubsection 4.13.2.3: Prescribed Isotropic Active Contraction