Anisotropic properties

where X, Y and Z are the parameters in respective directions. This can be applied to any parameter such as $\sigma ,\mathrm{\mu }$or $\lambda$.

Here is an example of thermal conductivity anisotropy for a Carbon-Fiber thermoplastic piece, with a lower thermal conductivity in the Z direction.

In this case we choose Expression as the parameter types and use:

This can be also used for a slice case with no changes in the expression.

where, Rx, Ry, Rz are rotation about that axis in radians.

Example on how to rotate tensor:

In this example thermal conductivity would be maximal along the line rotated 45 degrees (pi/4 radians) around Z axis.

Temperature dependance

It is also possible to use temperature dependance in the expression. It should be noted as a*$1, where ‘a’ corresponds to some value but $1 represents the temperature value in the node in degrees Celsius.

So the expression would look something like:

Where you can see for the Y value $1 has been used.

2D cases

You can also use expressions for 2D cases. In this case, nothing has to be changed.

Note that Z direction is redundant as the 2D case happens in XY plane.

So you can input the same value as for the 3D case or just a 0, it will not change the result.

For example, if you want to have a small conductivity in radial direction but a large one in axial direction, you could input something like this:

In this case the Z component is not relevant but it is still necessary to have – it has been input as 0.

If all 3 components have not been input in the expression, the simulation will end with an error.