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
defaultDrainedLinearTEC	real64	0	Default Linear Thermal Expansion Coefficient of the Solid Rock Frame
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
defaultYoungModulusAxial	real64	-1	Default Axial Young’s Modulus
defaultYoungModulusTransverse	real64	-1	Default Transverse Young’s Modulus
name	groupName	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>