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.

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

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

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.

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.