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: $F_{f i b e r} = |\frac{σ_{1}}{X}|$ $F_{f i b e r} = |\frac{σ_{1}}{X}|$; Where $X = X_{T}$ $X = X_{T}$ or $X = X_{C}$ $X = X_{C}$ if $σ_{1} \geq 0$ $σ_{1} \geq 0$ or $σ_{1} < 0$ $σ_{1} < 0$
Matrix Failure: $F_{m a t r i x} = {(\frac{σ_{2}}{Y})}^{2} + {(\frac{τ_{12}}{S})}^{2}$ $F_{m a t r i x} = {(\frac{σ_{2}}{Y})}^{2} + {(\frac{τ_{12}}{S})}^{2}$; Where $Y = Y_{T}$ $Y = Y_{T}$ or $Y = X Y_{C}$ $Y = X Y_{C}$ if $σ_{2} \geq 0$ $σ_{2} \geq 0$ or; The final failure is given as:; $F_{i n d e x} = \max [F_{f i b e r}, F_{m a t r i x}]$ $F_{i n d e x} = \max [F_{f i b e r}, F_{m a t r i x}]$

Fiber Failure: $F_{f i b e r} = |\frac{σ_{1}}{X}|$ $F_{f i b e r} = |\frac{σ_{1}}{X}|$; Where $X = X_{T}$ $X = X_{T}$ or $X = X_{C}$ $X = X_{C}$ if $σ_{1} \geq 0$ $σ_{1} \geq 0$ or $σ_{1} < 0$ $σ_{1} < 0$
Matrix Failure: $F_{m a t r i x} = \frac{σ_{2}^{2}}{Y_{T} Y_{C}} + {(\frac{τ_{12}}{S})}^{2} + (\frac{1}{Y_{T}} - \frac{1}{Y_{C}}) σ_{2}$ $F_{m a t r i x} = \frac{σ_{2}^{2}}{Y_{T} Y_{C}} + {(\frac{τ_{12}}{S})}^{2} + (\frac{1}{Y_{T}} - \frac{1}{Y_{C}}) σ_{2}$; The final failure is given as:; $F_{i n d e x} = \max [F_{f i b e r}, F_{m a t r i x}]$ $F_{i n d e x} = \max [F_{f i b e r}, F_{m a t r i x}]$

Fiber Failure

F_{f i b e r} = |\frac{σ_{1}}{X}|

$F_{f i b e r} = |\frac{σ_{1}}{X}|$

Where

X = X_{T}

$X = X_{T}$ or

X = X_{C}

$X = X_{C}$ if

σ_{1} \geq 0

$σ_{1} \geq 0$ or

σ_{1} < 0

$σ_{1} < 0$

Matrix Failure

Three failures modes are developed:

Mode A: When $σ_{2} > 0$ $σ_{2} > 0$; $F_{m a t r i x}^{A} = \sqrt{{(\frac{τ_{12}}{S})}^{2} + {(1 - P_{⊥ | |}^{+} \frac{Y_{T}}{S})}^{2} {(\frac{σ_{2}}{Y_{T}})}^{2}} + P_{⊥ | |}^{+} \frac{σ_{2}}{S}$ $F_{m a t r i x}^{A} = \sqrt{{(\frac{τ_{12}}{S})}^{2} + {(1 - P_{⊥ | |}^{+} \frac{Y_{T}}{S})}^{2} {(\frac{σ_{2}}{Y_{T}})}^{2}} + P_{⊥ | |}^{+} \frac{σ_{2}}{S}$
Mode B: When $σ_{2} < 0$ $σ_{2} < 0$ and $0 \leq |\frac{σ_{2}}{τ_{12}}| \leq \frac{R_{⊥ ⊥}^{A}}{|τ_{21 c}|}$ $0 \leq |\frac{σ_{2}}{τ_{12}}| \leq \frac{R_{⊥ ⊥}^{A}}{|τ_{21 c}|}$; $F_{m a t r i x}^{B} = \frac{1}{S} (\sqrt{τ_{12}^{2} + {(P_{⊥ | |}^{-} σ_{2})}^{2}} + P_{⊥ | |}^{-} σ_{2})$ $F_{m a t r i x}^{B} = \frac{1}{S} (\sqrt{τ_{12}^{2} + {(P_{⊥ | |}^{-} σ_{2})}^{2}} + P_{⊥ | |}^{-} σ_{2})$
Mode C: Otherwise; $F_{m a t r i x}^{C} = [{(\frac{τ_{12}}{2 (1 + P_{⊥ ⊥}^{-}) S})}^{2} + {(\frac{σ_{2}}{Y_{C}})}^{2}] \frac{Y_{C}}{- (σ_{2})}$ $F_{m a t r i x}^{C} = [{(\frac{τ_{12}}{2 (1 + P_{⊥ ⊥}^{-}) S})}^{2} + {(\frac{σ_{2}}{Y_{C}})}^{2}] \frac{Y_{C}}{- (σ_{2})}$

Where, for all the above equations we define:

R_{⊥ ⊥}^{A} = \frac{S}{2 P_{⊥ | |}^{-}} (\sqrt{1 + 2 P_{⊥ | |}^{-} \frac{Y_{C}}{S}} - 1)

$R_{⊥ ⊥}^{A} = \frac{S}{2 P_{⊥ | |}^{-}} (\sqrt{1 + 2 P_{⊥ | |}^{-} \frac{Y_{C}}{S}} - 1)$

τ_{21 c} = S \sqrt{1 + 2 P_{⊥ ⊥}^{-}}

$τ_{21 c} = S \sqrt{1 + 2 P_{⊥ ⊥}^{-}}$

P_{⊥ ⊥}^{-} = P_{⊥ | |}^{-} \frac{R_{⊥ ⊥}^{A}}{S}

$P_{⊥ ⊥}^{-} = P_{⊥ | |}^{-} \frac{R_{⊥ ⊥}^{A}}{S}$

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

PuckFT(tensor,xt,xc,yt,yc,s,criterion,output2d,sets,plies,elems,parts,props,pool_name,layer_index,opt_str)

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).