Dielectric

Dielectric

A piezoelectric material responds to an electric potential gradient by straining, while stress causes an electric potential gradient in the material (see Piezoelectricity). The material also has a dielectric property so that an electrical charge exists when the material has a potential gradient.

The electrical behavior is defined by

where $q_i$ is the electric “displacement” vector, $e_{ijk}^{\phi }$ is the material's piezoelectric stress coefficient matrix, defining the stress ${\sigma }_{ij}$ caused by the electrical potential gradient $E_j$ in a fully constrained material (it can also be interpreted as the electrical displacement $q_i$ caused by the applied strain ${\epsilon }_{ij}$ at a zero electrical potential gradient), and $D_{ij}^{\phi \left(e\right)}$ is the material's dielectric property.

The dielectric matrix can be isotropic, orthotropic, or fully anisotropic. For nonisotropic dielectric materials a local orientation for the material directions must be specified. The entries of the dielectric matrix refer to what is more commonly known in the literature as the permittivity of the material.

• Isotropic: $D_{ij}^{\phi \left(e\right)}=D^{\phi \left(e\right)}{\delta }_{ij}$ , you specify the single value $D^{\phi \left(e\right)}$ .
• Orthotropic: You specify three values in the dielectric matrix, $(D_{11}^{\phi \left(e\right)},D_{22}^{\phi \left(e\right)},D_{33}^{\phi \left(e\right)})$
• Anisotropic: You specify six values in the dielectric matrix, $(D_{11}^{\phi \left(e\right)},D_{12}^{\phi \left(e\right)},D_{22}^{\phi \left(e\right)},D_{13}^{\phi \left(e\right)},D_{23}^{\phi \left(e\right)},D_{33}^{\phi \left(e\right)})$

Table 1. Type=Isotropic

Input Data	Description
Dielectric Constant	Dielectric constant $D^{\phi \left(e\right)}$ .
Use temperature-dependent data	Specify material parameters that depend on temperature. A Temperature field appears in the data table.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Table 2. Type=Orthotropic

Input Data	Description
D11, D22, and D33	Dielectric constants $(D_{11}^{\phi \left(e\right)},D_{22}^{\phi \left(e\right)},D_{33}^{\phi \left(e\right)})$ .
Use temperature-dependent data	Specify material parameters that depend on temperature. A Temperature field appears in the data table.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Table 3. Type=Anisotropic

Input Data	Description
D11, D12, D13 D21, D22, D23 D31, D32, D33	Dielectric constants $(D_{11}^{\phi \left(e\right)},D_{12}^{\phi \left(e\right)},D_{22}^{\phi \left(e\right)},D_{13}^{\phi \left(e\right)},D_{23}^{\phi \left(e\right)},D_{33}^{\phi \left(e\right)})$ .
Use temperature-dependent data	Specify material parameters that depend on temperature. A Temperature field appears in the data table.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.