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
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	string	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>