# Hashin Criterion

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

The implementation1is:
• Fiber Tension ${\text{σ}}_{1}>0$

${F}_{fiber}^{T}={\left(\frac{{\text{σ}}_{1}}{{X}_{T}}\right)}^{2}+{\left(\frac{{\text{τ}}_{12}}{S}\right)}^{2}$

• Fiber Compression ${\sigma }_{1}<0$

${F}_{fiber}^{C}=\left|\frac{{\text{σ}}_{1}}{{X}_{C}}\right|$

• Matrix Tension ${\sigma }_{2}>0$

${F}_{matrix}^{T}={\left(\frac{{\sigma }_{2}}{{Y}_{T}}\right)}^{2}+{\left(\frac{{\tau }_{12}}{S}\right)}^{2}$

• Matrix Compression ${\sigma }_{2}<0$

${F}_{matrix}^{C}={\left(\frac{{\text{σ}}_{2}}{2S}\right)}^{2}+{\left(\frac{{\text{τ}}_{12}}{S}\right)}^{2}+\left[{\left(\frac{{\text{σ}}_{2}}{2S}\right)}^{2}-1\right]\frac{{\text{σ}}_{2}}{{Y}_{C}}$

## Syntax

HashinFT(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 specifying failure mode. Option can be Fiber or Matrix.

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

${F}_{index}=\mathrm{max}\left[{F}_{fiber},{F}_{matrix}\right]$

1 Formula implemented in HyperView core are reported.