Expansion

Thermal expansion describes the induction of mechanical strains in material in response to changes in temperature (and, in the case of fluid flow analyses, buoyancy strains as well). The option requires the definition of the thermal expansion coefficients.

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Thermal Expansion

Thermal expansion effects:

  • can be isotropic, orthotropic, fully anisotropic, or transversely isotropic;
  • are defined as the total expansion from a reference temperature, and;
  • can be specified as a function of temperature and/or predefined field variables.

Thermal Expansion

The thermal expansion generates strains according to the formula

ε t h = α ( θ , f β ) ( θ − θ 0 ) − α ( θ I , f β I ) ( θ I − θ 0 )
where α ( θ , f β ) is the thermal expansion coefficient, θ is the current temperature, θ I is the initial temperature, f β are the current values of the predefined field variables, f β I are the initial values of the predefined field variables, and θ 0 is the reference temperature for the thermal expansion coefficient. The second term in the above equation represents the strain due to the difference between the initial temperature, θ I , and the corresponding reference temperature, θ 0 . This term is necessary to enforce the assumption that there is no initial thermal strain for cases in which the reference temperature does not equal the corresponding initial temperature.

The thermal expansion definition can be isotropic, orthotropic, anisotropic, or transversely isotropic. Orthotropic and anisotropic thermal expansion can be used only with materials where the material directions are defined with local orientations.

  • Isotropic: Specify one value α .
  • Orthotropic: Specify three values, ( α 11 ⁢   , α 22 ⁢   , α 33   )
  • Anisotropic: Specify six values, ( α 11 ⁢   , α 22 ⁢   , α 33   ,   α 12 ⁢   , α 23 ⁢   , α 13 )
  • Transversely Isotropic: Specify two values, ( α t ⁢   , α n ⁢   )

Table 1. Reference Temperature
Input Data Description
Reference Temperature Reference temperature, θ 0 .
Table 2. Type=Isotropic
Input Data Description
Thermal Expansion Coefficient Expansion coefficient, α .
Use temperature-dependent data Specifies material parameters that depend on temperature. A Temperature temperature 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=Orthotropic
Input Data Description
ALPHA11, ALPHA22, ALPHA33 Expansion coefficients, ( α 11 ⁢   , α 22 ⁢   , α 33   ) .
Use temperature-dependent data Specifies material parameters that depend on temperature. A Temperature temperature 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 4. Type=Anisotropic
Input Data Description
ALPHA11, ALPHA22, ALPHA33, ALPHA12, ALPHA13, ALPHA23 Expansion coefficients, ( α 11 ⁢   , α 22 ⁢   , α 33   ,   α 12 ⁢   , α 23 ⁢   , α 13 ) .
Use temperature-dependent data Specifies material parameters that depend on temperature. A Temperature temperature 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 5. Type=Transversely Isotropic
Input Data Description
Parallel coefficient of expansion Expansion coefficient, α t ⁢   .
Normal coefficient of expansion Expansion coefficients, α n ⁢   .
Use temperature-dependent data Specifies material parameters that depend on temperature. A Temperature temperature 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.