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Subsection 4.1.1: Specifying Fiber Orientation or Material Axes Up Subsection 4.1.1: Specifying Fiber Orientation or Material Axes Subsubsection 4.1.1.2: Orthotropic Materials

#### 4.1.1.1 Transversely Isotropic Materials

For transversely isotropic materials fiber orientation is specified with the fiber element. This element takes one attribute, namely type, which specifies the type of the fiber generator. The possible values are specified in the following table.
 type Value Description local Use local element numbering (1) vector Define the fiber orientation as a constant vector (2) spherical specifies a spherical fiber distribution (3) cylindrical specifies a cylindrical fiber distribution (4) angles Specifies the fiber direction using spherical angles (5)
If the type attribute is omitted, the fiber distribution will follow the local element nodes 1 and 2. This would be the same as setting the fiber attribute to local and setting the value to “1,2”.
1. In this case, the fiber direction is determined by local element node numbering. The value is interpreted as the local node numbers of the nodes that define the direction of the fiber. The following example defines a local fiber axis by local element nodes 1 and 2. This option is very useful when the local fiber direction can be interpreted as following one of the mesh edges.
<fiber type="local">1,2</fiber>


local fiber direction option
2. The fiber orientation is specified by a vector. The value is the direction of the fiber. The following defines all element fiber directions in the direction of the vector [1,0,0]:
<fiber type="vector">1,0,0</fiber>


vector fiber direction option
3. The fiber orientation is determined by a point in space and the global location of each element integration point. The value is the location of the point. The following example defines a spherical fiber distribution centered at [0,0,1]:
<fiber type="spherical">0,0,1</fiber>


spherical fiber direction option
4. cylindrical: This type generates a fiber distribution that is cylindrical. The following subparameters must be defined.
centerdefines the center of the cylinder
axis defines the axis of the cylinder
vector defines a vector that will be transported around the cylinder
<fiber type="cylindrical">
<center>0,0,0</center>
<axis>0,0,1</axis>
<vector>0,1,0</vector>
</fiber>

5. angles: This type generates a fiber orientation via the specification of spherical angles (azimuth and declination) relative to the local material axes (or global coordinate system, if no local material axes are defined). The following subparameters must be defined.
thetaazimuth angle (in degrees)
phi declination angle (in degrees)

Spherical angles
The fiber is oriented along where are orthonormal vectors representing the local element coordinate system (when specified, Section 4.1.1.2↓), or global coordinate system.
<fiber type="angles">
<theta>20</center>
<phi>90</phi>
</fiber>

When specifying a fiber direction , FEBio generates a set of orthogonal material axes as described in Section 4.1.1.2↓. generated with , or else if is collinear with (where the triple refers to unit vectors defining the global coordinate system, i.e. , etc.). Because of the non-uniqueness of these material axes (only is along a uniquely defined direction in a fiber element), caution should be used when material axes are compounded, as may occur in nested materials such as solid mixtures described in Sections 4.1.2.14↓ & 4.1.3.22↓. To enforce uniqueness, use the mat_axis element instead of the fiber element.
Subsection 4.1.1: Specifying Fiber Orientation or Material Axes Up Subsection 4.1.1: Specifying Fiber Orientation or Material Axes Subsubsection 4.1.1.2: Orthotropic Materials