Fabric Law for Elastic Orthotropic Shells (LAW19 and LAW58)
Two elastic linear models and a nonlinear model exist in Radioss.
Fabric Linear Law for Elastic Orthotropic Shells (LAW19)
A material is orthotropic if its behavior is symmetrical with respect to two orthogonal plans. The fabric law enables to model this kind of behavior. This law is only available for shell elements and can be used to model an airbag fabric. Many of the concepts for this law are the same as for LAW14 which is appropriate for composite solids. If axes 1 and 2 represent the orthotropy directions, the constitutive matrix $C$ is defined in terms of material properties:
where the subscripts denote the orthotropy axes. As the matrix $C$ is symmetric:
- ${E}_{11}$
- Young's modulus in direction 1
- ${E}_{22}$
- Young's modulus in direction 2
- $\upsilon $ _{12}
- Poisson's ratio
- ${G}_{12}$ , ${G}_{23}$ , ${G}_{31}$
- Shear moduli for each direction
The coordinates of a global vector $\overrightarrow{V}$ is used to define direction 1 of the local coordinate system of orthotropy.
Fabric Nonlinear Law for Elastic Anisotropic Shells (LAW58)
This law is used with Radioss standard shell elements and anisotropic layered property (TYPE16). The fiber directions (warp and weft) define the local axes of anisotropy. Material characteristics are determined independently in these axes. Fibers are nonlinear elastic and follow the equation:
The shear in fabric material is only supposed to be function of the angle between current fiber directions (axes of anisotropy):
and
${G}_{A}=({G}_{0}-G)\mathrm{tan}({\alpha}_{T})$ , $G=\frac{{G}_{T}}{1+{\mathrm{tan}}^{2}({\alpha}_{T})}$ with ${\tau}_{0}={G}_{0}\mathrm{tan}({\alpha}_{0})$
- ${\alpha}_{T}$
- Shear lock angle
- ${G}_{T}$
- Tangent shear modulus at ${\alpha}_{T}$
- ${G}_{0}$
- Shear modulus at $\alpha $ = 0
If ${G}_{0}$ = 0, the default value is calculated to avoid shear modulus discontinuity at ${\alpha}_{T}$ : ${G}_{0}$ = $G$ .
Where, ${\alpha}_{0}$ is an initial angle between fibers defined in the shell property (TYPE16).