Modeling Anisotropic Materials

Anisotropic materials respond differently to an excitation depending on its direction. Because excitations are generally vectors and the corresponding response is a vector density, material properties are usually rank-2 tensor densities. For example, the following material properties are anisotropic tensor densities: diffusion coefficient, permittivity, thermal conductivity, and electrical conductivity.

These properties are, in principle, specified in matrix form and defined by their components in the coordinate system selected in the node settings. At most four components are used in 2D and at most nine components in 3D. When the material contains symmetries, you can specify only a few coefficients which are expanded to a matrix using the following patterns:

•	Isotropic (the default) — enter only one value c.

•	Diagonal — enter the diagonal components for an anisotropic material with the main axes aligned with the model’s coordinate system.

•	Symmetric — enter a symmetric matrix using the diagonal components and the upper off-diagonal components.

•	Anisotropic — enter the full 2-by-2 (2D) or 3-by-3 (3D) matrix for an anisotropic material: