orthotropic elastic

Module: solid

Category: material

Type string: "orthotropic elastic"

Parameters

Name	Description	Default	Units
density	density	1	[M/L^3]
E1	E1 modulus	0	[P]
E2	E2 modulus	0	[P]
E3	E3 modulus	0	[P]
G12	G12 shear modulus	0	[P]
G23	G23 shear modulus	0	[P]
G31	G31 shear modulus	0	[P]
v12	v12	0	[]
v23	v23	0	[]
v31	v31	0	[]
mat_axis			[]

Description

The material type for orthotropic elasticity is orthotropic elastic.

The stress-strain relation for this material is given by

\[ \left[\begin{array}{c} E_{11}\\ E_{22}\\ E_{33}\\ 2E_{23}\\ 2E_{31}\\ 2E_{12} \end{array}\right]=\left[\begin{array}{cccccc} 1/E_{1} & -\nu_{21}/E_{2} & -\nu_{31}/E_{3} & 0 & 0 & 0\\ -\nu_{12}/E_{1} & 1/E_{2} & -\nu_{32}/E_{3} & 0 & 0 & 0\\ -\nu_{13}/E_{1} & -\nu_{23}/E_{2} & 1/E_{3} & 0 & 0 & 0\\ 0 & 0 & 0 & 1/G_{23} & 0 & 0\\ 0 & 0 & 0 & 0 & 1/G_{31} & 0\\ 0 & 0 & 0 & 0 & 0 & 1/G_{12} \end{array}\right]\left[\begin{array}{c} T_{11}\\ T_{22}\\ T_{33}\\ T_{23}\\ T_{31}\\ T_{12} \end{array}\right] \]

Example:

<material id="3" type="orthotropic elastic">
  <mat_axis type="vector">
    <a>0.866,0.5,0</a>
    <d>-0.5,0.866,0</d>
  </mat_axis>
  <E1>1</E1>
  <E2>2</E2>
  <E3>3</E3>
  <v12>0</v12>
  <v23>0</v23>
  <v31>0</v31>
  <G12>1</G12>
  <G23>1</G23>
  <G31>1</G31>
</material>