#### Command list

• Input handling
• Solution control and techniques
• Output
• Mesh commands
• Nodes and connectivity
• Material properties
• Initial conditions
• Boundary conditions
• Loads
• Contact and tied interfaces
• Rigid bodies
• Connectors
• Parameters and functions
• Geometries
• Sets
• Coordinate system
• Particle
• SPH

### MAT_ORTHOTROPIC

###### Material properties
*MAT_ORTHOTROPIC
"Optional title"
mid, $\rho$, $E_1$, $E_2$, $G_{12}$, $\nu_{12}$, $\nu_{23}$
$c$, $c_{dec}$, $X_t$, $X_c$, $Y_t$, $Y_c$, $\beta$, $S$
erode, $res$

#### Parameter definition

VariableDescription
mid Unique material identification number
$\rho$ Density
$E_1$ Young's modulus in fiber direction
$E_2$ Young's modulus orthogonally to fiber direction
$G_{12}$ In-plane shear modulus
$\nu_{12}$ Poisson's ratio
$\nu_{23}$ Poisson's ratio
$c$ Strain rate sensitivity parameter
$c_{dec}$ Strain rate sensitivity decay coefficient
$X_t$ Ultimate tensile stress in fiber direction
$X_c$ Ultimate compressive stress in fiber direction
$Y_t$ Ultimate tensile stress orthogonally to fiber direction
$Y_c$ Ultimate compressive stress orthogonally to fiber direction
$\beta$ Failure parameter
$S$ Failure parameter
erode Element erosion flag
options:
0 $\rightarrow$ failed element is not eroded
1 $\rightarrow$ failed element is eroded
$res$ Residual strength after failure
default: 0

#### Description

This is an orthotropic composite model. The stress can be expressed as:

$\mathbf{\sigma} = \mathbf{L} : \mathbf{\epsilon} + \displaystyle{ \frac{c}{c_{dec}} \int_0^t \dot{\mathbf{\epsilon}}(\tau) \cdot \mathrm{e}^{(\tau-t)/c_{dec}} \mathrm{d}\tau }$

where $\mathbf{L}$ is the tangential stiffness of the material (fourth order tensor). There are four different failure criteria.

Fiber tension/shear if $\sigma_{11} \gt 0$:

$D_1 = (\sigma_{11}/X_t)^2 + \beta(\vert \tau_{12} \vert / S)$

Fiber compression if $\sigma_{11} \lt 0$:

$D_2 = (\sigma_{11}/X_c)^2$

Matrix tension if $\sigma_{22} \gt 0$:

$D_3 = (\sigma_{22}/Y_t)^2 + \beta(\vert \tau_{12} \vert / S)$

Matrix compression/shear if $\sigma_{22} \lt 0$:

$D_4 = (\sigma_{11}/X_c)^2 + ( (Y_c/2S)^2 - 1) (\sigma_{22}/Y_c) + (\tau_{12}/S)^2$

All stresses are reduced with the factor $res$ at fiber failure, i.e. if $D_1 \ge 1$. $D_2 \ge 1$ indicates fiber buckling whereby compressive fiber stresses $(\sigma_{11})$ and in plane shear stresses $(\tau_{12})$ are reduced with the factor $res$. $D_3 \ge 1$ or $D_4 \ge 1$ indicates matrix failure and $\sigma_{22}$ and $\tau_{12}$ are reduced with the factor $res$.

Initial fiber directions need to be defined using either INITIAL_MATERIAL_DIRECTION, INITIAL_MATERIAL_DIRECTION_VECTOR or INITIAL_MATERIAL_DIRECTION_WRAP.