Field Coupling: Field Expansion Options

Field expansion effects:

are analogous to thermal expansion effects that induce mechanical strains in response to changes in temperature fields;
can be isotropic, orthotropic, or fully anisotropic;
are defined as total expansion from a reference value of the predefined field variable;
are only supported in implicit analyses;
can be specified as a function of temperature and/or predefined field variables, and;
can be defined for more than one predefined field variable.

Field Expansion

The field expansion for each specified field generates field expansion strains according to the formula

ε^{f} = α_{f} (θ, f_{β}) (f_{β} - f_{n}^{0}) - α_{f} (θ^{I}, f_{β}^{I}) (f_{n}^{I} - f_{n}^{0})

where

α_{f} (θ, f_{β})

is the field expansion coefficient,

f_{n}

is the current value of the predefined field variable

n

f_{n}^{I}

is the initial value of the predefined field variable

n

f_{β}

are the current values of the predefined field variables,

f_{β}^{I}

are the initial values of the predefined field variables, and

f_{n}^{0}

is the reference value of the predefined field variable

n

for the field expansion coefficient. The second term in the above equation represents the strain due to the difference between the initial value of the predefined field variablen,

f_{n}^{I}

, and the corresponding reference value,

f_{n}^{0}

. This term is necessary to enforce the assumption that there is no initial field expansion strain for cases in which the reference value of the predefined field variable n does not equal the corresponding initial value.

The field expansion definition can be isotropic, orthotropic, or fully anisotropic. Orthotropic and anisotropic field expansion can be used only with materials where the material directions are defined with local orientations. Only isotropic field expansion is allowed with the hyperelastic and hyperfoam material models.

Isotropic: You specify the single value $α_{f}$ .
Orthotropic: You must specify three values in the dielectric matrix, $(α_{f_{11}}, α_{f_{22}}, α_{f_{33}})$
Anisotropic: You must specify six values in the dielectric matrix, $(α_{f_{11}}, α_{f_{22}}, α_{f_{33}}, α_{f_{12}}, α_{f_{13}}, α_{f_{23}})$

Table 1. Type=Isotropic
Input Data	Description
Field Expansion Coefficient	Expansion coefficient, $α_{f}$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
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
ALPHA11, ALPHA22, ALPHA33	Expansion coefficients, $(α_{f_{11}}, α_{f_{22}}, α_{f_{33}})$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
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
ALPHA11, ALPHA22, ALPHA33, ALPHA12, ALPHA13, ALPHA23	Expansion coefficients, $(α_{f_{11}}, α_{f_{22}}, α_{f_{33}}, α_{f_{12}}, α_{f_{13}}, α_{f_{23}})$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
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.