# About orientation of anisotropic materials

## Reminder

The isotropic materials are characterized by constitutive laws independent of the direction of the applied field.

The anisotropic materials are characterized by constitutive laws dependent on the direction of the applied field.

## Consequence

An anisotropic material must be oriented in the region to which it is assigned.

## Various models

The models, provided in Flux for various physical properties of materials, are divided (mostly * ) into two versions:

• for an isotropic material: the model is a scalar model
• for an anisotropic material: the model is a tensor model

(with description of the model on each axis)

A description of the models called double, i.e. for the two types of materials (isotropic / anisotropic), is presented in the tables below:
• Double models for the B(H), J(E), D(E) behavior laws:

B(H) J(E) D(E)
All models, except Saturation in 3D All models, except Superconductivity All models
• Double models for the k(T) thermal conductivity:

k(T)
All models
• Double models for the B(H,T), J(E,T), D(E,T) behavior laws depending on temperature:

B(H, T) J(E, T) D(E, T)
No model Constant resistivity No model

• Linear function of T
• Exponential function of T

## Orientation: principle

For an anisotropic material, the physical properties are defined with respect to the axes of a virtual coordinate system.

To orient an anisotropic material in a region, it is necessary to choose a coordinate system (real coordinate system) for orientation.

The principle of orientation of an anisotropic (magnetic) material in a region is presented in the figure below:

Flux also proposes an angle for the definition of the orientation in the XOY plane: θ angle.

## !!! Anisotropic material and thin or filiform regions

Everything that was previously presented concerns the massive regions (volume regions in 3D / face regions in 2D).

The models for anisotropic materials cannot be used for thin regions or filiform regions.