# Puck Criteria (2D)

HyperView Composite libraries expose different flavors of the general criterion of PUCK failure theory for 2D plane stress.

## Simple Puck

Fiber Failure
${F}_{fiber}=\left|\frac{{\text{σ}}_{1}}{X}\right|$
Where $\text{X}={X}_{T}$ or $\text{X}={X}_{C}$ if ${\text{σ}}_{1}\ge 0$ or ${\text{σ}}_{1}<0$
Matrix Failure
${F}_{matrix}={\left(\frac{{\text{σ}}_{2}}{Y}\right)}^{2}+{\left(\frac{{\text{τ}}_{12}}{S}\right)}^{2}$
Where $Y={Y}_{T}$ or $Y=X{Y}_{C}$ if ${\sigma }_{2}\ge 0$ or
The final failure is given as:
${F}_{index}=\mathrm{max}\left[{F}_{fiber},{F}_{matrix}\right]$

## Modified Puck

Fiber Failure
${F}_{fiber}=\left|\frac{{\sigma }_{1}}{X}\right|$
Where $\text{X}={X}_{T}$ or $\text{X}={X}_{C}$ if ${\text{σ}}_{1}\ge 0$ or ${\text{σ}}_{1}<0$
Matrix Failure
${F}_{matrix}=\frac{{\text{σ}}_{2}^{2}}{{Y}_{T}{Y}_{C}}+{\left(\frac{{\text{τ}}_{12}}{S}\right)}^{2}+\left(\frac{1}{{Y}_{T}}-\frac{1}{{Y}_{C}}\right){\text{σ}}_{2}$
The final failure is given as:
${F}_{index}=\mathrm{max}\left[{F}_{fiber},{F}_{matrix}\right]$

## Puck2D

Fiber Failure
${F}_{fiber}=\left|\frac{{\sigma }_{1}}{X}\right|$
Where $\text{X}={X}_{T}$ or $\text{X}={X}_{C}$ if ${\text{σ}}_{1}\ge 0$ or ${\text{σ}}_{1}<0$
Matrix Failure
Three failures modes are developed:
Mode A
When ${\sigma }_{2}>0$
${F}_{matrix}^{A}=\sqrt{{\left(\frac{{\text{τ}}_{12}}{S}\right)}^{2}+{\left(1-{P}_{\perp ||}^{+}\frac{{Y}_{T}}{S}\right)}^{2}{\left(\frac{{\text{σ}}_{2}}{{Y}_{T}}\right)}^{2}}+{P}_{\perp ||}^{+}\frac{{\text{σ}}_{2}}{S}$
Mode B
When ${\sigma }_{2}<0$ and $0\le \left|\frac{{\text{σ}}_{2}}{{\text{τ}}_{12}}\right|\le \frac{{R}_{\perp \perp }^{A}}{\left|{\text{τ}}_{21c}\right|}$
${F}_{matrix}^{B}=\frac{1}{S}\left(\sqrt{{\text{τ}}_{12}^{2}+{\left({P}_{\perp ||}^{-}{\text{σ}}_{2}\right)}^{2}}+{P}_{\perp ||}^{-}{\text{σ}}_{2}\right)$
Mode C
Otherwise
${F}_{matrix}^{C}=\left[{\left(\frac{{\text{τ}}_{12}}{2\left(1+{P}_{\perp \perp }^{-}\right)S}\right)}^{2}+{\left(\frac{{\text{σ}}_{2}}{{Y}_{C}}\right)}^{2}\right]\frac{{Y}_{C}}{-\left({\text{σ}}_{2}\right)}$
Where, for all the above equations we define:
${R}_{\perp \perp }^{A}=\frac{S}{2{P}_{\perp ||}^{-}}\left(\sqrt{1+2{P}_{\perp ||}^{-}\frac{{Y}_{C}}{S}}-1\right)$
${\text{τ}}_{21c}=S\sqrt{1+2{P}_{\perp \perp }^{-}}$
${P}_{\perp \perp }^{-}={P}_{\perp ||}^{-}\frac{{R}_{\perp \perp }^{A}}{S}$
Being and , in Puck’s theory, the inclination parameters respectively on the tension and compression side.
The following values are used:
GFRP CFRP OTHERWISE
0.25 0.30 0.2
0.30 0.35 0.3

## Syntax

PuckFT(tensor,xt,xc,yt,yc,s,criterion,output2d,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
criterion
Puck Criterion: simple, modified, General2D, Glass2D, Carbon2D (D=simple)
output2d
Puck 2D output mode: value or mode (0=fiber failure, 1,2,3=matrix failure mode A,B,C) (D=value)
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).