Hashin Criterion

The Hashin criterion gives conditions to distinguish between matrix or fiber failure by tension or compression.

The implementation¹is:

Fiber Tension $σ_{1} > 0$ $σ_{1} > 0$
$F_{f i b e r}^{T} = {(\frac{σ_{1}}{X_{T}})}^{2} + {(\frac{τ_{12}}{S})}^{2}$ $F_{f i b e r}^{T} = {(\frac{σ_{1}}{X_{T}})}^{2} + {(\frac{τ_{12}}{S})}^{2}$
Fiber Compression $σ_{1} < 0$ $σ_{1} < 0$
$F_{f i b e r}^{C} = |\frac{σ_{1}}{X_{C}}|$ $F_{f i b e r}^{C} = |\frac{σ_{1}}{X_{C}}|$
Matrix Tension $σ_{2} > 0$ $σ_{2} > 0$
$F_{m a t r i x}^{T} = {(\frac{σ_{2}}{Y_{T}})}^{2} + {(\frac{τ_{12}}{S})}^{2}$ $F_{m a t r i x}^{T} = {(\frac{σ_{2}}{Y_{T}})}^{2} + {(\frac{τ_{12}}{S})}^{2}$
Matrix Compression $σ_{2} < 0$ $σ_{2} < 0$
$F_{m a t r i x}^{C} = {(\frac{σ_{2}}{2 S})}^{2} + {(\frac{τ_{12}}{S})}^{2} + [{(\frac{σ_{2}}{2 S})}^{2} - 1] \frac{σ_{2}}{Y_{C}}$ $F_{m a t r i x}^{C} = {(\frac{σ_{2}}{2 S})}^{2} + {(\frac{τ_{12}}{S})}^{2} + [{(\frac{σ_{2}}{2 S})}^{2} - 1] \frac{σ_{2}}{Y_{C}}$

Syntax

HashinFT(tensor,xt,xc,yt,yc,s,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
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 specifying failure mode. Option can be Fiber or Matrix.

If opt_str is not passed, the resultant failure index is reported as:

$F_{i n d e x} = \max [F_{f i b e r}, F_{m a t r i x}]$ $F_{i n d e x} = \max [F_{f i b e r}, F_{m a t r i x}]$

Formula implemented in HyperView core are reported.