# Hill Criterion

Calculates the ply failure index according to the Hill (Tsai-Hill) theory.

${\text{F}}_{\text{index}}=\frac{{\text{σ}}_{1}^{2}}{{\text{X}}^{2}}-\frac{{\text{σ}}_{1}{\text{*σ}}_{2}}{{\text{X}}^{2}}+\frac{{\text{σ}}_{2}^{2}}{{\text{Y}}^{2}}+\frac{{\text{τ}}_{12}^{2}}{{\text{S}}^{2}}$

Where, the failure parameters $X$ and $Y$ depends on the considered quadrant of the coordinate plane, being $\text{X}={X}_{T}$ or $\text{X}={X}_{C}$ if ${\text{σ}}_{1}\ge 0$ or ${\text{σ}}_{1}<0$ and the same for $Y$ .

## Syntax

HillFT(tensor,xt,xc,yt,yc,s,sets,plies,elems,parts,props,pool_name,layer_index,opt_str)

## Arguments

tensor
Stress table
xt
Allowable tensile stress in ply material direction 1
xc
Allowable compressive stress in ply material direction 1
yt
Allowable tensile stress in ply material direction 2
yc
Allowable compressive stress in ply material direction 2
s
Allowable in-plane shear stress
sets
Set table (D=NULL)
plies
Ply table (D=NULL)
elems
Element table (D)
parts
Part table (D)
props
Property table (D)
pool_name
Pool name (D=@current_pool)
layer_index
Layer index (D=@current_slice_index)
opt_str
This is an optional argument, which can passed if needed (D=option).