Conductivity

A material's thermal conductivity:

must be defined for Uncoupled Heat Transfer Analysis, Fully Coupled Thermal-Stress Analysis, and Coupled Thermal-Electrical Analysis;
can be linear or nonlinear (by defining it as a function of temperature);
can be isotropic, orthotropic, or fully anisotropic; and
can be specified as a function of temperature and field variables.

This page discusses:

Directional Dependence of Thermal Conductivity
Elements

Directional Dependence of Thermal Conductivity

Isotropic, orthotropic, or fully anisotropic thermal conductivity can be defined. Only isotropic thermal conductivity can be defined for an incompressible fluid dynamic analysis that includes an energy equation. For orthotropic or anisotropic thermal conductivity, a local orientation (Orientations) must be used to specify the material directions used to define the conductivity.

Isotropic Conductivity

For isotropic conductivity, only one value of conductivity is required at each temperature and field variable value. Isotropic conductivity is the default.

Input File Usage

CONDUCTIVITY, TYPE=ISO

Abaqus/CAE Usage

Property module: material editor: ThermalConductivity: Type: Isotropic

Orthotropic Conductivity

For orthotropic conductivity three values of conductivity ( $k_{11}$ , $k_{22}$ , $k_{33}$ ) are required at each temperature and field variable value.

Input File Usage

CONDUCTIVITY, TYPE=ORTHO

Abaqus/CAE Usage

Property module: material editor: ThermalConductivity: Type: Orthotropic

Transversely Isotropic Conductivity

A special subclass of orthotropy is transverse isotropy, which is characterized by a plane of isotropy at every point in the material. Abaqus assumes the 2–3 plane to be the plane of isotropy at every point; therefore, $k_{22} = k_{33}$ and only two values of conductivity ( $k_{11}$ , $k_{22}$ ) are required at each temperature and field variable value.

Input File Usage

CONDUCTIVITY, TYPE=TRANSVERSELY ISOTROPIC

Abaqus/CAE Usage

Computing conductivity for a transversely isotropic material is not supported in Abaqus/CAE.

Anisotropic Conductivity

For fully anisotropic conductivity six values of conductivity ( $k_{11}$ , $k_{12}$ , $k_{22}$ , $k_{13}$ , $k_{23}$ , $k_{33}$ ) are required at each temperature and field variable value.

Input File Usage

CONDUCTIVITY, TYPE=ANISO

Abaqus/CAE Usage

Property module: material editor: ThermalConductivity: Type: Anisotropic

Conductivity for a Short-Fiber Reinforced Composite

Abaqus/Standard computes conductivity of a short-fiber reinforced composite using orientation averaging of a unidirectional composite with transversely isotropic conductivity ( $k_{L}$ , $k_{T}$ ):

k_{11} = (k_{L} - k_{T}) \cdot a_{1} + k_{T}, k_{22} = (k_{L} - k_{T}) \cdot a_{2} + k_{T}, k_{33} = (k_{L} - k_{T}) \cdot a_{3} + k_{T},

where

a_{1}

a_{2}

, and

a_{3}

are the maximum, mid, and minimum principal values of a second-order orientation tensor describing fiber dispersion at the material point.

Input File Usage

CONDUCTIVITY, TYPE=ORTHO
FIBER DISPERSION

Abaqus/CAE Usage

Computing conductivity for a short-fiber reinforced composite is not supported in Abaqus/CAE.

Elements

Thermal conductivity is active in all heat transfer, coupled temperature-displacement, coupled thermal-electrical-structural, and coupled thermal-electrical elements in Abaqus. Thermal conductivity for a short-fiber reinforced composite is supported only in Abaqus/Standard.