Material Properties
Until now, there has only been a formal introduction of the constitutive relations. These seemingly simple relations can be quite complicated at times. There are four main groups of materials for which they require some consideration. A given material can belong to one or more of these groups.
Inhomogeneous Materials
Inhomogeneous materials are the least complicated. An inhomogeneous medium is one in which the constitutive parameters vary with the space coordinates so that different field properties prevail at different parts of the material structure.
Anisotropic Materials
For anisotropic materials, the field relationships at any point differ for different directions of propagation. This means that a 3-by-3 tensor is necessary to properly define the constitutive relationships. If this tensor is symmetric, the material is often referred to as reciprocal. In such cases, rotate the coordinate system such that a diagonal matrix results. If two of the diagonal entries are equal, the material is uniaxially anisotropic. If none of the elements have the same value, the material is biaxially anisotropic (Ref. 2). Anisotropic parameters are needed, for example, to examine permittivity in crystals (Ref. 2) and when working with conductivity in solenoids.
Nonlinear Materials
Nonlinearity is the effect of variations in permittivity or permeability with the intensity of the electromagnetic field. Nonlinearity also includes hysteresis effects where not only the current field intensities influence the physical properties of the material, but also the history of the field distribution.
Dispersive Materials
Dispersion describes changes in a wave’s velocity with wavelength. In the frequency domain, dispersion is expressed with a frequency dependence of the constitutive relations.
Material Properties and the Material Browser
All interfaces in the AC/DC Module support the use of the COMSOL Multiphysics material libraries. The typical electromagnetic material properties that can be stored are:
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The electrical conductivity
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The relative permittivity
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The relative permeability
The physics-specific domain material properties are by default taken from the material specification. The material properties are inputs to material laws or constitutive relations that are defined on the feature level below the physics interface node in the model tree. There is one editable default domain feature that initially represents a linear isotropic material. Domains with different material laws are specified by adding additional features. Some of the domain parameters can either be a scalar or a matrix (tensor) depending on whether the material is isotropic or anisotropic.
In a similar way, boundary, edge, and point settings are specified by adding the corresponding features. A certain feature might require one or several fields to be specified, while others generate the conditions without user-specified fields.
For detailed information about Materials and Modeling Anisotropic Materials, including the Electromagnetic Models, see the COMSOL Multiphysics Reference Manual.