MAT_FABRIC

Material properties

*MAT_FABRIC
"Optional title"
mid, $\rho$, $E$, $\nu$
$E_f$, $\varepsilon_l$, $\varepsilon_{f0}$, $\varepsilon_{f1}$, $\varepsilon_e$, $\sigma_y$, $K_n$, $n$
$\alpha_1$, $\alpha_2$, $\alpha_3$, $\alpha_4$, $\eta_1$, $\eta_2$, $\eta_3$, $\eta_4$
$\mu$, $\xi$, $c$, $\dot{\varepsilon}_0$, $W_c$

Parameter definition

Variable
Description
mid
Unique material identification number
$\rho$
Density
$E$
Young's modulus (matrix)
$\nu$
Poisson's (matrix)
$E_f$
Fiber stiffness
$\varepsilon_l$
Fiber locking strain (woven fabrics)
$\varepsilon_{f0}$
Strain where fibers begin to fail
$\varepsilon_{f1}$
Strain where all fibers have failed
$\varepsilon_e$
Element erosion strain
$\sigma_y$
Matrix yield stress
$K_n$
Optional non-linear bulk stiffness parameter
$n$
Optional non-linear bulk stiffness exponent
$\alpha_1$
Fiber angle 1
$\alpha_2$
Fiber angle 2
$\alpha_3$
Fiber angle 3
$\alpha_4$
Fiber angle 4
$\eta_1$
Fiber fill fraction 1
$\eta_2$
Fiber fill fraction 2
$\eta_3$
Fiber fill fraction 3
$\eta_4$
Fiber fill fraction 4
$\mu$
Dynamic viscosity
$\xi$
Initial stiffness (fraction of fiber stiffness)
$c$
Strain rate parameter
$\dot{\varepsilon}_0$
Reference strain rate
$W_c$
Matrix failure parameter
default: no matrix failure

Description

This is a model for fiber reinforced composites. Fibers can be defined in up to four different directions. Fiber stress, damage and failure is computed individually for each fiber direction.

A fiber stress, $\sigma_i$, is calculated as:

$\sigma_i = \left\{ \begin{array}{lcl} \displaystyle{ sf \cdot \xi \cdot \varepsilon_i } & : & \varepsilon_i \leq 0 \\ \displaystyle{ sf \cdot \left( \frac{1-\xi}{2} \cdot \frac{\varepsilon_i^2}{\varepsilon_l} + \xi \cdot \varepsilon_i \right) } & : & 0 \lt \varepsilon_i \leq \varepsilon_l \\ \displaystyle{ sf \cdot \left( \frac{\xi-1}{2} \cdot \varepsilon_l + \varepsilon_i \right) } & : & \varepsilon_i \gt \varepsilon_l \end{array} \right. $

where:

$sf = \left(1-D_i^2\right) \cdot E_f$
Fiber stress strain relationship
Fiber stress strain relationship

$\xi$ is the ratio between initial and full tensile stiffness for the in-plane directions. $\varepsilon_i$ is the fiber strain in the direction $i$ and $\varepsilon_i$ is the locking strain. $\varepsilon_l$ is used when modeling weaves, where initial straining of the material leads to realigning of the fibers rather than strething. $\eta_i$ is the volume fraction fibers and $D_i$ is the fiber damage level which grows irreversibly from 0 to 1:

$D_i = \left\{ \begin{array}{lcl} \displaystyle{ 0 } & : & \varepsilon_i^{max} \leq \varepsilon_{f0} \\ \displaystyle{ \frac{\varepsilon_i^{max} - \varepsilon_{f0}}{\varepsilon_{f1} - \varepsilon_{f0}} } & : & \varepsilon_{f0} \lt \varepsilon_i^{max} \leq \varepsilon_{f1} \\ \displaystyle{ 1 } & : & \varepsilon_i^{max} \gt \varepsilon_{f1} \\ \end{array} \right. $

where $\varepsilon_i^{max}$ is the largest tensile strain the fibers have experienced. $\varepsilon_{f0}$ defines when fibers begin to fail and $\varepsilon_{f1}$ defines when all fibers have failed. The failure strains can be defined to be strain rate dependent:

$\displaystyle{ \varepsilon_{f0}^{sr} = \varepsilon_{f0} \cdot \left(1 + \frac{\dot{\varepsilon}_i}{\dot{\varepsilon}_0} \right)^c }$
$\displaystyle{ \varepsilon_{f1}^{sr} = \varepsilon_{f1} \cdot \left(1 + \frac{\dot{\varepsilon}_i}{\dot{\varepsilon}_0} \right)^c }$

The pressure in the material is calculated as:

$p = \left\{ \begin{array}{lcl} \displaystyle{ -K \cdot \varepsilon_v } & : & \varepsilon_v \geq 0 \\ \displaystyle{ -K \cdot \varepsilon_v + \sum_{i = 1}^4 \eta_i \cdot K_n \cdot \vert \varepsilon_v \vert ^n } & : & \varepsilon_v \lt 0 \\ \end{array} \right. $

where $K$ is the bulk modulus of the matrix and $K_n$ and $n$ are input parameters controlling the non-linear response in compression.

The total stress in the material is defined as:

$\displaystyle{ \boldsymbol{\sigma} = 2 G \boldsymbol{\varepsilon}_{dev}^e - p \mathbf{I} + \sum_{i=1}^4 \eta_i \sigma_i \mathbf{v}_i \otimes \mathbf{v}_i + 2 \mu \dot{\boldsymbol{\varepsilon}}_{dev} }$

where $\boldsymbol{\varepsilon}_{dev}^e$ is the deviatoric elastic strain in the matrix material, $\dot{\boldsymbol{\varepsilon}}_{dev}$ is the total deviatoric strain rate and $\mathbf{v}_i$ is a fiber direction.

Matrix damage evolves with plastic flow in tension:

$\displaystyle{\dot D = \frac{\mathrm{max}(0, \sigma_1) \cdot \dot\varepsilon_{eff}^p}{W_c}}$

$\sigma_1$ is the maximum principal stress in the matrix and $\dot\varepsilon_{eff}^p$ is the effective plastic strain rate. The matrix loses its ability to carry shear loads when $D=1$.

The initial fabric orientation needs to be defined using either INITIAL_MATERIAL_DIRECTION, INITIAL_MATERIAL_DIRECTION_VECTOR or INITIAL_MATERIAL_DIRECTION_WRAP.

The effective geometric erosion strain $\varepsilon_e$ is used to remove distorted elements, but it is only active for elements where all fiber directions have failed.

Example

Blast loaded Dyneema panel

Dyneema panel in a test rig exposed to blast loading.

*UNIT_SYSTEM SI *PARAMETER s = 0.05, "stand-off distance" d = 0.05, "charge diameter" h = 0.01, "charge thickness, h=1cm is 36g for 5cm diameter" tend = 0.01 *TIME [%tend] *OUTPUT_SENSOR "Center" 1, 1, 0.0, 0.0, -0.024 *INCLUDE mesh.k *CHANGE_P-ORDER ALL, 0, 3 *PART "Dyneema" 1, 1 "Rig" 2, 2 *MAT_FABRIC "Dyneema" 1, 980.0, 5.0e8, 0.45 115.0e9, 0.0, 0.037, 0.037, 1.0, 20.0e6, 400.0e9, 1.5 0, 90, 0, 0, 0.415, 0.415, 0, 0 250.0, 0.125, 0.05, 100.0 *INITIAL_MATERIAL_DIRECTION_VECTOR 1, P, 1 1, 0, 0, 0, 1, 0 *MAT_RIGID "Rig" 2, 7850 *BC_MOTION "Rig" 1 P, 2, XYZ, XYZ *CONTACT "All to all" 1 ALL, 0, ALL, 0, 0.4 *PARTICLE_DOMAIN ALL, 0, 100000 -0.3, -0.3, -0.2, 0.3, 0.3, 0.2 *PARTICLE_AIR 1, AIR, 1 *PARTICLE_HE 2, PETN, 2 *GEOMETRY_BOX "Air" 1 -0.3, -0.3, -0.2, 0.3, 0.3, 0.2 *GEOMETRY_PIPE "Charge" 2 0.0, 0.0, [%s], 0.0, 0.0, [%s+%h], [%d/2] *PARTICLE_DETONATION "Booster" 1 0.0, 0.0, [%s+%h/2] *END