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:

$F_{index}=\max \left[F_{fiber},F_{matrix}\right]$

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:

$F_{index}=\max \left[F_{fiber},F_{matrix}\right]$

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 ${\sigma }_2>0$

$F_{matrix}^A=\sqrt{{\left(\frac{{\text{τ}}_{12}}{S}\right)}^2+{\left(1-P_{\perp \left|\right|}^{+}\frac{Y_T}{S}\right)}^2{\left(\frac{{\text{σ}}_2}{Y_T}\right)}^2}+P_{\perp \left|\right|}^{+}\frac{{\text{σ}}_2}{S}$

Mode B

When ${\sigma }_2<0$ and $0\le \left|\frac{{\text{σ}}_2}{{\text{τ}}_{12}}\right|\le \frac{R_{\perp \perp }^A}{\left|{\text{τ}}_{21c}\right|}$

$F_{matrix}^B=\frac{1}{S}\left(\sqrt{{\text{τ}}_{12}^2+{\left(P_{\perp \left|\right|}^{-}{\text{σ}}_2\right)}^2}+P_{\perp \left|\right|}^{-}{\text{σ}}_2\right)$

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:

$R_{\perp \perp }^A=\frac{S}{2P_{\perp \left|\right|}^{-}}\left(\sqrt{1+2P_{\perp \left|\right|}^{-}\frac{Y_C}{S}}-1\right)$

${\text{τ}}_{21c}=S\sqrt{1+2P_{\perp \perp }^{-}}$

$P_{\perp \perp }^{-}=P_{\perp \left|\right|}^{-}\frac{R_{\perp \perp }^A}{S}$

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).