# 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.

- Nonlinear function (
`fct_ID`_{i}) curve to define the warp, weft and shear behavior - Young's modulus, soften coefficient
`B`, straightening strain`S`_{i}and fiber bending modulus reduction factor`Flex`_{i}In warp and weft direction:

${\sigma}_{ii}={E}_{i}{\epsilon}_{ii}-\frac{({B}_{i}{\epsilon}_{ii}{}^{2})}{2}\text{(}i=1,2)\text{when}\frac{d\sigma}{d\epsilon}0$

${\sigma}_{ii}={\mathrm{max}}_{{\epsilon}_{ii}}\left({E}_{i}{\epsilon}_{ii}-\frac{({B}_{i}{\epsilon}_{ii}{}^{2})}{2}\right)\text{(}i=1,2)\text{when}\frac{d\sigma}{d\epsilon}\le 0$

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

`G`_{T}to describe the strengthening.$\tau ={G}_{0}\mathrm{tan}(\alpha )-{\tau}_{0}$ if $\alpha \le {\alpha}_{T}$

$\tau =\frac{{G}_{T}}{1+{\mathrm{tan}}^{2}({\alpha}_{T})}\mathrm{tan}(\alpha )+\left({G}_{0}-\frac{{G}_{T}}{1+{\mathrm{tan}}^{2}({\alpha}_{T})}\right)\mathrm{tan}({\alpha}_{T})-{\tau}_{0}$ if $\alpha >{\alpha}_{T}$

In LAW58, use `Flex`_{i} to
describe this behavior:

`S`

_{i}is reached), then normal fiber elasticity

`E`

_{i}could be used.