Elastic properties

Four types are supported.

Isotropic

type="isotropic"

<materials>
  ...
  <material name="iso1" type="isotropic">
    <elastic>
      <e>...</e>
      <nu>...</nu>
    </elastic>
  </material>
  ...
</materials>

Specification

• 2 constants: e and nu.

Transversely isotropic

type="transversely isotropic"

For the transversely isotropic material, the code internally fills the remaining five orthotropic constants as follows when they are not provided explicitly:

• e3   = e2

• nu13 = nu12

• nu23 = 0.3 (arbitrary fallback — supply it explicitly for accuracy)

• g13  = g12

• g23  = e3 / (2 * (1 + nu23))

<materials>
  ...
  <material name="lam1" type="transversely isotropic">
    <elastic>
      <e1>...</e1>
      <e2>...</e2>
      <nu12>...</nu12>
      <g12>...</g12>
      <!-- e3, nu13, nu23, g13, g23 are optional; defaults are derived -->
    </elastic>
  </material>
  ...
</materials>

Specification

• 4 required constants: e1, e2, g12, nu12. Internally converted to an orthotropic material. Optional overrides for e3, nu13, nu23, g13, g23 are accepted; defaults are listed above.

---

Orthotropic

type="orthotropic" or type="engineering"

<materials>
  ...
  <material name="orth1" type="orthotropic">
    <elastic>
      <e1>...</e1>
      <e2>...</e2>
      <e3>...</e3>
      <g12>...</g12>
      <g13>...</g13>
      <g23>...</g23>
      <nu12>...</nu12>
      <nu13>...</nu13>
      <nu23>...</nu23>
    </elastic>
  </material>
  ...
</materials>

Specification

• 9 constants: e1, e2, e3, g12, g13, g23, nu12, nu13, nu23.

---

Anisotropic

type="anisotropic"

<materials>
  ...
  <material name="aniso1" type="anisotropic">
    <elastic>
      <c11>...</c11>
      <c12>...</c12>
      <c13>...</c13>
      <c14>...</c14>
      <c15>...</c15>
      <c16>...</c16>
      <c22>...</c22>
      <c23>...</c23>
      <c24>...</c24>
      <c25>...</c25>
      <c26>...</c26>
      <c33>...</c33>
      <c34>...</c34>
      <c35>...</c35>
      <c36>...</c36>
      <c44>...</c44>
      <c45>...</c45>
      <c46>...</c46>
      <c55>...</c55>
      <c56>...</c56>
      <c66>...</c66>
    </elastic>
  </material>
  ...
</materials>

Specification

• 21 constants: c11, c12, c13, c14, c15, c16, c22, c23, c24, c25, c26, c33, c34, c35, c36, c44, c45, c46, c55, c56, c66. These constants are defined as:

\[\begin{split} \begin{Bmatrix} \sigma_{11} \\ \sigma_{12} \\ \sigma_{13} \\ \sigma_{22} \\ \sigma_{23} \\ \sigma_{33} \end{Bmatrix} = \begin{bmatrix} c_{11} & c_{12} & c_{13} & c_{14} & c_{15} & c_{16} \\ c_{12} & c_{22} & c_{23} & c_{24} & c_{25} & c_{26} \\ c_{13} & c_{23} & c_{33} & c_{34} & c_{35} & c_{36} \\ c_{14} & c_{24} & c_{34} & c_{44} & c_{45} & c_{46} \\ c_{15} & c_{25} & c_{35} & c_{45} & c_{55} & c_{56} \\ c_{16} & c_{26} & c_{36} & c_{46} & c_{56} & c_{66} \end{bmatrix} \begin{Bmatrix} \epsilon_{11} \\ 2\epsilon_{12} \\ 2\epsilon_{13} \\ \epsilon_{22} \\ 2\epsilon_{23} \\ \epsilon_{33} \end{Bmatrix} \end{split}\]