Model: Elastic Orthotropic

Overview

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

$\begin{bmatrix} \sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{23} \\ \sigma_{13} \\ \sigma_{12} \end{bmatrix} = \begin{bmatrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\ C_{12} & C_{22} & C_{23} & 0 & 0 & 0 \\ C_{13} & C_{23} & C_{33} & 0 & 0 & 0 \\ 0 & 0 & 0 & C_{44} & 0 & 0 \\ 0 & 0 & 0 & 0 & C_{55} & 0 \\ 0 & 0 & 0 & 0 & 0 & C_{66} \end{bmatrix} \begin{bmatrix} \epsilon_{11} \\ \epsilon_{22} \\ \epsilon_{33} \\ 2\epsilon_{23} \\ 2\epsilon_{13} \\ 2\epsilon_{12} \end{bmatrix}.$

This system contains nine 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 C11 Component of Voigt Stiffness Tensor
defaultC12	real64	-1	Default C12 Component of Voigt Stiffness Tensor
defaultC13	real64	-1	Default C13 Component of Voigt Stiffness Tensor
defaultC22	real64	-1	Default C22 Component of Voigt Stiffness Tensor
defaultC23	real64	-1	Default C23 Component of Voigt Stiffness Tensor
defaultC33	real64	-1	Default C33 Component of Voigt Stiffness Tensor
defaultC44	real64	-1	Default C44 Component of Voigt Stiffness Tensor
defaultC55	real64	-1	Default C55 Component of Voigt Stiffness Tensor
defaultC66	real64	-1	Default C66 Component of Voigt Stiffness Tensor
defaultDensity	real64	required	Default Material Density
defaultDrainedLinearTEC	real64	0	Default Linear Thermal Expansion Coefficient of the Solid Rock Frame
defaultE1	real64	-1	Default Young’s Modulus E1
defaultE2	real64	-1	Default Young’s Modulus E2
defaultE3	real64	-1	Default Young’s Modulus E3
defaultG12	real64	-1	Default Shear Modulus G12
defaultG13	real64	-1	Default Shear Modulus G13
defaultG23	real64	-1	Default Shear Modulus G23
defaultNu12	real64	-1	Default Poission’s Ratio Nu12
defaultNu13	real64	-1	Default Poission’s Ratio Nu13
defaultNu23	real64	-1	Default Poission’s Ratio Nu23
name	groupName	required	A name is required for any non-unique nodes

Example

A typical Constititutive block will look like:

<Constitutive>
  <ElasticOrthotropic
     name="shale"
     defaultDensity="2700"
     defaultNu12="0.20"
     defaultNu13="0.25"
     defaultNu23="0.30"
     defaultE1="40.0e6"
     defaultE2="50.0e6"
     defaultE3="60.0e6"
     defaultG12="20.0e6"
     defaultG13="30.0e6"
     defaultG23="40.0e6" />
</Constitutive>