Model: Elastic Transverse-Isotropic¶

Overview¶

This model may be used for solid materials with a linear elastic, transverse-isotropic behavior. This is most readily expressed in Voight notation as

$\begin{bmatrix} \sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{23} \\ \sigma_{13} \\ \sigma_{12} \end{bmatrix} = \begin{bmatrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\ C_{12} & C_{11} & C_{13} & 0 & 0 & 0 \\ C_{13} & C_{13} & C_{33} & 0 & 0 & 0 \\ 0 & 0 & 0 & C_{44} & 0 & 0 \\ 0 & 0 & 0 & 0 & C_{44} & 0 \\ 0 & 0 & 0 & 0 & 0 & (C_{11}-C_{12})/2 \end{bmatrix} \begin{bmatrix} \epsilon_{11} \\ \epsilon_{22} \\ \epsilon_{33} \\ 2\epsilon_{23} \\ 2\epsilon_{13} \\ 2\epsilon_{12} \end{bmatrix}.$

This system contains five independent constants. These constants are calculated from the input parameters indicated below.

Parameters¶

The following attributes are supported. The “default” keyword in front of certain properties indicates that this is the default value adopted for a region unless the user separately specifies a heterogeneous field via the FieldSpecification mechanism.

Name	Type	Default	Description
defaultC11	real64	-1	Default Stiffness Parameter C11
defaultC13	real64	-1	Default Stiffness Parameter C13
defaultC33	real64	-1	Default Stiffness Parameter C33
defaultC44	real64	-1	Default Stiffness Parameter C44
defaultC66	real64	-1	Default Stiffness Parameter C66
defaultDensity	real64	required	Default Material Density
defaultPoissonRatioAxialTransverse	real64	-1	Default Axial-Transverse Poisson’s Ratio
defaultPoissonRatioTransverse	real64	-1	Default Transverse Poisson’s Ratio
defaultShearModulusAxialTransverse	real64	-1	Default Axial-Transverse Shear Modulus
defaultThermalExpansionCoefficient	real64	0	Default Thermal Expansion Coefficient
defaultYoungModulusAxial	real64	-1	Default Axial Young’s Modulus
defaultYoungModulusTransverse	real64	-1	Default Transverse Young’s Modulus
name	string	required	A name is required for any non-unique nodes

Example¶

A typical Constititutive block will look like:

<Constitutive>
  <ElasticTransverseIsotropic
     name="shale"
     defaultDensity="2700"
     defaultPoissonRatioAxialTransverse="0.20"
     defaultPoissonRatioTransverse="0.30"
     defaultYoungModulusAxial="50.0e6"
     defaultYoungModulusTransverse="60.0e6"
     defaultShearModulusAxialTransverse="30.0e6" />
</Constitutive>