Hoffman Criterion

The resulting failure index in Hoffman’s theory for an orthotropic lamina in a general state of plane stress (2D) with unequal tensile and compressive strengths is given by:

Findex=1XT1XCσ1+1YT1YCσ2+σ12XTXC+σ22YTYCσ1σ2XTXC+τ122S2 MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@7758@

Where:
  • Xt,Xc MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8qacaWGybGaamiDaiaacYcacaWGybGaam4yaaaa@3A5F@ are the maximum allowable stresses in the 1-direction in tension and compression,
  • Yt,Yc MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8qacaWGzbGaamiDaiaacYcacaWGzbGaam4yaaaa@3A61@ are the maximum allowable stresses in the 2-direction in tension and compression,
  • S MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8qacaWGtbaaaa@36EC@ is the allowable in-plane shear stress

Syntax

HoffmanFT(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, which can passed if needed (D=option).