# LAW19 and LAW58 for Fabric

Radioss has two material laws for modeling fabrics LAW19 and LAW58. LAW19 is an elastic orthotropic material and must be used with /PROP/TYPE9. LAW58 is hyperelastic anisotropic fabric material and must be used with /PROP/TYPE16.

Coupling between warp and weft directions could be defined in this material law to reproduce physical interaction between fibers. Both material laws are often used for airbag modeling.

In LAW58, two methods are provided to define the stress-strain behavior.
• Nonlinear function (fct_IDi) curve to define the warp, weft and shear behavior
• Young's modulus, soften coefficient B, straightening strain Si and fiber bending modulus reduction factor Flexi

In warp and weft direction:

For in-plane shear in initial state, use ${G}_{0}$ . Once α (angle between wrap and weft) reaches ${\alpha }_{T}$ (shear lock angle), then use GT to describe the strengthening.

$\tau ={G}_{0}\mathrm{tan}\left(\alpha \right)-{\tau }_{0}$ if $\alpha \le {\alpha }_{T}$

$\tau =\frac{{G}_{T}}{1+{\mathrm{tan}}^{2}\left({\alpha }_{T}\right)}\mathrm{tan}\left(\alpha \right)+\left({G}_{0}-\frac{{G}_{T}}{1+{\mathrm{tan}}^{2}\left({\alpha }_{T}\right)}\right)\mathrm{tan}\left({\alpha }_{T}\right)-{\tau }_{0}$ if $\alpha >{\alpha }_{T}$
For out-of-plane shear stress-strain is described with ${G}_{sh}$ .
For fabric, there is straight process at the beginning of tension. At this phase, fiber shows very soft, due to not being tightened yet.
In LAW58, use Flexi to describe this behavior:(1)
${E}_{fi}=Fle{x}_{i}*{E}_{i}$
After the fabric is tight (strengthening strain Si is reached), then normal fiber elasticity Ei could be used.