"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
Variable | Description |
---|---|
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 |
$res$ | Residual strength after failure |
Description
This is an orthotropic composite model. The stress can be expressed as:
$\boldsymbol{\sigma} = \mathbf{L} : \boldsymbol{\varepsilon} + \displaystyle{ \frac{c}{c_{dec}} \int_0^t \dot{\boldsymbol{\varepsilon}}(\tau) \cdot \mathrm{e}^{(\tau-t)/c_{dec}} \mathrm{d}\tau }$
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.