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:

F index = 1 X T 1 X C σ 1 + 1 Y T 1 Y C σ 2 + σ 1 2 X T X C + σ 2 2 Y T Y C σ 1 σ 2 X T X C + τ 12 2 S 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaBaaaleaapeGaamyAaiaad6gacaWGKbGaamyzaiaa dIhaa8aabeaak8qacqGH9aqpdaqadaWdaeaapeWaaSaaa8aabaWdbi aaigdaa8aabaWdbiaadIfapaWaaSbaaSqaa8qacaWGubaapaqabaaa aOWdbiabgkHiTmaalaaapaqaa8qacaaIXaaapaqaa8qacaWGybWdam aaBaaaleaapeGaam4qaaWdaeqaaaaaaOWdbiaawIcacaGLPaaacaqG dpWdamaaBaaaleaapeGaaGymaaWdaeqaaOWdbiabgUcaRmaabmaapa qaa8qadaWcaaWdaeaapeGaaGymaaWdaeaapeGaamywa8aadaWgaaWc baWdbiaadsfaa8aabeaaaaGcpeGaeyOeI0YaaSaaa8aabaWdbiaaig daa8aabaWdbiaadMfapaWaaSbaaSqaa8qacaWGdbaapaqabaaaaaGc peGaayjkaiaawMcaaiaabo8apaWaaSbaaSqaa8qacaaIYaaapaqaba GcpeGaey4kaSYaaSaaa8aabaWdbiaabo8apaWaa0baaSqaa8qacaaI Xaaapaqaa8qacaaIYaaaaaGcpaqaa8qacaWGybWdamaaBaaaleaape GaamivaaWdaeqaaOWdbiaadIfapaWaaSbaaSqaa8qacaWGdbaapaqa baaaaOWdbiabgUcaRmaalaaapaqaa8qacaqGdpWdamaaDaaaleaape GaaGOmaaWdaeaapeGaaGOmaaaaaOWdaeaapeGaamywa8aadaWgaaWc baWdbiaadsfaa8aabeaak8qacaWGzbWdamaaBaaaleaapeGaam4qaa Wdaeqaaaaak8qacqGHsisldaWcaaWdaeaapeGaae4Wd8aadaWgaaWc baWdbiaaigdaa8aabeaak8qacaqGdpWdamaaBaaaleaapeGaaGOmaa WdaeqaaaGcbaWdbiaadIfapaWaaSbaaSqaa8qacaWGubaapaqabaGc peGaamiwa8aadaWgaaWcbaWdbiaadoeaa8aabeaaaaGcpeGaey4kaS YaaSaaa8aabaWdbiaabs8apaWaa0baaSqaa8qacaaIXaGaaGOmaaWd aeaapeGaaGOmaaaaaOWdaeaapeGaam4ua8aadaahaaWcbeqaa8qaca aIYaaaaaaaaaa@7758@

Where:
  • Xt,Xc MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGybGaamiDaiaacYcacaWGybGaam4yaaaa@3A5F@ are the maximum allowable stresses in the 1-direction in tension and compression,
  • Yt,Yc MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGzbGaamiDaiaacYcacaWGzbGaam4yaaaa@3A61@ are the maximum allowable stresses in the 2-direction in tension and compression,
  • S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGtbaaaa@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).